A small town has two local high schools. High School A currently has 850 students
and is projected to grow by 45 students each year. High School B currently has 1000
students and is projected to grow by 35 students each year. Let A represent the
number of students in High School A in t years, and let B represent the number of
students in High School B after t years. Write an equation for each situation, in terms
of t, and determine how many students would be in each high school in the year they
are projected to have the same number of students.
A =
Answer:
Submit Answer
B
=
attempt 2 out of 2
pls help!!

Por lo tanto, la respuesta es correcta. La empresa tenía 95 kilogramos de materia prima disponible.

Para resolver este problema, debemos utilizar una ecuación matemática. Si llamamos "x" a la cantidad de materia prima disponible, podemos escribir:

0.4x + 57 = x

La primera parte de la ecuación representa el 40% de la materia prima consumida por la empresa (0.4x), mientras que la segunda parte representa la cantidad de materia prima que le queda después de consumir ese 40% (x). Si resolvemos esta ecuación, encontraremos el valor de "x":

0.6x = 57
x = 95

Por lo tanto, la empresa tenía 95 kilogramos de materia prima disponible. Podemos comprobar esto sustituyendo el valor de "x" en la ecuación original:

0.4(95) + 57 = 95
38 + 57 = 95
95 = 95

Por lo tanto, la respuesta es correcta. La empresa tenía 95 kilogramos de materia prima disponible.

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Talisa is a college student and is seeking mental health services on her campus. Talisa is most likely to be seen by a counselor or mental health professional at her college campus.

College campuses typically have counseling centers or mental health services available for students. These services are often staffed by licensed professionals such as counselors, therapists, psychologists, or psychiatrists. The specific type of mental health professional Talisa will be seen by may depend on the resources and staff available at her particular college.

However, the initial point of contact for mental health services on campus is often a counselor or therapist who can provide counseling, support, and referrals for additional care if needed. These professionals are trained to address a wide range of mental health concerns commonly experienced by college students, such as stress, anxiety, depression, and adjustment difficulties. They play a crucial role in supporting students' mental well-being during their college years.

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The Weighted Average Cost of Capital (WACC) for Starbucks' new project can be determined by considering the subjective approach. To calculate the WACC, information such as the cost of equity and the cost of debt is required, along with their respective weights in the company's capital structure.

In this scenario, the given information only mentions Starbucks' overall WACC, which is 12%. However, to determine the WACC for the new project, additional details specific to the project, such as its risk profile and capital structure, are necessary. Without this specific information, it is not possible to calculate the WACC for the new project. The WACC is influenced by various factors, including the riskiness of the project, the expected return on equity and debt, and the proportion of equity and debt in the project's capital structure. Therefore, a comprehensive evaluation of the project's risk and financial structure is required to determine an accurate WACC for the new project.

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If Regan plays on the school softball team.she gets a hit 20% of the time. it is  48.8% likely that Regan will get at least one hit in the game.

To calculate the probability that Regan will get at least one hit in three at-bats we can use the concept of complementary probability.

Probability of not getting a hit in a single at-bat = 1 - 0.20

Probability of not getting a hit in a single at-bat  = 0.80

Probability of not getting a hit in three consecutive at-bats= (0.80)³

Probability of not getting a hit in three consecutive at-bats = 0.512

Probability of getting at least one hit = 1 - 0.512

Probability of getting at least one hit = 0.488 or 48.8%.

Therefore it is  48.8% likely that Regan will get at least one hit in the game.

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The differentiation of the function with respect to x is 36x³ - 78x² + 78x - 36.

Given that, the function is (x - 1)³(3x - 2)².

Differentiating the function with respect to x, we get

(x - 1)³(3x - 2)² = 3(x - 1)²(3x - 2)² + (3x - 2)²(6x - 6)

= 3(x - 1)²(6x² - 4x + 4) + (3x² - 4x + 2)(6x - 6)

= 18x³ - 54x² + 54x - 24 + 18x³ - 24x² + 24x - 12

= 36x³ - 78x² + 78x - 36

Therefore, the differentiation of the function with respect to x is 36x³ - 78x² + 78x - 36.

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A statement made by the nursing staff that indicates their lack of understanding of the role of case management is if they believe case managers are responsible only for direct patient care.

If a nursing staff member states that case managers are solely responsible for direct patient care, it indicates a misunderstanding of the role of case management. Case management involves a broader scope of responsibilities beyond direct patient care. Case managers serve as advocates and coordinators, collaborating with healthcare providers, patients, and their families to ensure comprehensive and efficient care delivery.

The role of case management includes tasks such as assessing patients' needs, developing individualized care plans, coordinating services, facilitating transitions of care, and ensuring interest throughout the healthcare journey. Case managers also play a crucial role in managing resources, including healthcare utilization and cost containment. They work closely with interdisciplinary teams to ensure the appropriate allocation of resources and services, promoting quality care and positive patient outcomes.

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The nurse leader conducts an education session for the nursing staff regarding case management. Which statement made by the nursing staff indicates they do not understand the role of case management?

Answer:

Step-by-step explanation:

Based on this sample, we can say with 90% confidence that the average amount of money spent on food by adults in Washington State is likely to be between $264.30 and $282.92 per month.

a) To determine if the requirements to build a confidence interval are met, we need to check if the following conditions are satisfied:

Random Sampling: The problem states that a random sample of 120 adults in Washington State was polled, which satisfies the random sampling condition.

Independence: It is assumed that the individuals in the sample are independent of each other, meaning that one person's response does not affect another person's response.

This assumption is reasonable for this situation.

Sample Size: The sample size is 120, which is greater than 30. When the sample size is large, the Central Limit Theorem applies, allowing us to use a normal distribution for the sampling distribution of the sample mean.

Normality: In order to use the normal distribution, the population distribution needs to be approximately normal or the sample size needs to be large. Since the population distribution is not specified, we will assume that the sample size of 120 is large enough for the Central Limit Theorem to apply.

b) The critical value for a 90% confidence interval can be obtained from the standard normal distribution table or a statistical software. For a 90% confidence level, the critical value is 1.645.

c) To compute the 90% confidence interval, we will use the following formula:

Confidence Interval = sample mean ± (critical value x standard deviation / sqrt(sample size))

Confidence Interval = $273.61 ± (1.645 x $61.59 / sqrt(120))

Confidence Interval = $273.61 ± (1.645 x $61.59 / 10.954)

Confidence Interval = $273.61 ± $9.31

The 90% confidence interval is approximately $264.30 to $282.92.

d) The 90% confidence interval for the amount of money spent on food by adults in Washington State ranges from approximately $264.30 to $282.92.

This means that we are 90% confident that the true population mean falls within this range. In other words, if we were to repeat this sampling process multiple times and construct 90% confidence intervals, we would expect about 90% of those intervals to contain the true population mean.

Therefore, based on this sample, we can say with 90% confidence that the average amount of money spent on food by adults in Washington State is likely to be between $264.30 and $282.92 per month.

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Step-by-step explanation:

solve for the value of y in the expression negative 3y minus negative 18

a. Switching from a production plan of 8,000 units to a plan of 10,000 units would result in an absorption costing operating income of $fill in the blank 2.

b. The difference in variable costing operating income between the two production plans can be calculated based on the change in the number of units produced.

a. To determine the absorption costing operating income, we need to consider both the fixed and variable costs. In absorption costing, fixed costs are allocated to each unit produced, while variable costs are directly attributed to the units. Given that the fixed costs are $40,000 and the variable cost per unit is $80, we can calculate the absorption costing operating income for each production plan

For the initial plan of 8,000 units:

Total fixed costs = $40,000

Total variable costs = 8,000 units * $80 per unit = $640,000

Total costs = Total fixed costs + Total variable costs = $40,000 + $640,000 = $680,000

For the revised plan of 10,000 units:

Total fixed costs remain the same at $40,000

Total variable costs = 10,000 units * $80 per unit = $800,000

Total costs = Total fixed costs + Total variable costs = $40,000 + $800,000 = $840,000

Absorption costing operating income = Sales - Total cost

b. Variable costing operating income differs between the two production plans as it only considers the variable costs directly associated with the units produced. In variable costing, fixed costs are treated as period costs and are not allocated to the units.

For the initial plan of 8,000 units:

Total variable costs = 8,000 units * $80 per unit = $640,000

For the revised plan of 10,000 units:

Total variable costs = 10,000 units * $80 per unit = $800,000

The difference in variable costing operating income between the two plans would be $800,000 - $640,000 = $160,000.

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{a}, {b}, {c}, {a, b}, {a, c} and {b, c} are proper subset of the set {a,b,c}.

A proper subset is a subset of a set that contains some, but not all, of the elements of the original set.

In the case of the set m = {a, b, c}, we can find all the proper subsets by considering all the possible combinations of its elements.

The possible proper subsets of m are:

{a}: This subset contains only the element 'a' from the original set m.

{b}: This subset contains only the element 'b' from the original set m.

{c}: This subset contains only the element 'c' from the original set m.

{a, b}: This subset contains both elements 'a' and 'b' from the original set m, but not 'c'.

{a, c}: This subset contains both elements 'a' and 'c' from the original set m, but not 'b'.

{b, c}: This subset contains both elements 'b' and 'c' from the original set m, but not 'a'.

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The quadrupled functions can be evaluated by transforming them into quadratic functions to solve for the roots as follows;

a. x = ±3, and x = ±3·i

b. x = ±√(5)·i

c. x = ±√3, and ±i·√2

Quadratic functions are functions that have an highest power of 2, and which can be expressed in the form; a·x² + b·x + c = 0, where; a ≠ 0, and a, b, and c are numbers.

The specified roots of the quadrupled functions which can be expressed as quadratic function can be found as follows;

a. x⁴ - 81 = 0

x⁴ - 81 = ((x²)² - 9²) = 0

The difference of two squares equation indicates;

((x²)² - 9²) = (x² - 9) × (x² + 9) = 0

x² = 9, and x² = -9

x = ±3 and x = ±3·i

b. The roots of x⁴ + 10·x² + 25 = 0 can be found by taking x² = a, therefore;

x⁴ + 10·x² + 25 = a² + 10·a + 25 = 0

a² + 10·a + 25 = (a + 5) × (a + 5) = 0

a = -5

Therefore; x² = a = -5

x = √(5)·i

c. x⁴ - 2·x² - 6 = 0

Let x² = a, we get;

a² - 2·a - 6 = 0

(a - 3) × (a + 2) = 0

Therefore; a = 3, and a = -2

x = √a = ±√(3) = ±i·√(2)

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The populations from which the samples are obtained must be normally distributed.

Sampling is done correctly. Observations for within and between groups must be independent.

The variances among populations must be equal (homoscedastic).

Data are interval or nominal.

The sequence that can be used to model this problem situation is an arithmetic sequence. In an arithmetic sequence, the difference between consecutive terms is constant.

To find the formula for the nth term of the sequence, we can use the formula for arithmetic sequences: an = a1 + (n - 1)d, where an represents the nth term, a1 is the first term, n is the position of the term, and d is the common difference.

In this case, the first term (a1) is 4, and the common difference (d) can be calculated by finding the difference between consecutive terms: d = 6 - 4 = 2.

Therefore, the formula for the nth term of the sequence is: an = 4 + (n - 1)2.

To predict the number of axis deer in year fifteen (n = 15), we substitute n = 15 into the formula: a15 = 4 + (15 - 1)2 = 4 + 14 * 2 = 4 + 28 = 32.

The prediction is that there will be 32 axis deer in year fifteen. This prediction might be reasonable depending on the specific factors affecting the deer population, such as food availability, predation, and hunting pressure. It is important to consider other variables that could influence the population dynamics of axis deer over time.

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The correct interpretation of the 90% confidence interval is: c) 90% of the time, Kat can be certain that the calculated interval (22.96, 26.64) accurately represents the real average number of eggs that chickens on this farm lay.

What is confidence interval?

An predicted range of values for the true population parameter is known as a confidence interval.

The calculation for the 90% confidence interval can be done using the formula:

Confidence Interval = Sample Mean ± (Critical Value * Standard Deviation / √(Sample Size))

Given:

Sample Mean (x) = 24.8 eggs

Standard Deviation (σ) = 6.9 eggs

Sample Size (n) = 40

Confidence Level = 90%

For a 90% confidence level, the critical value is approximately 1.645.

Now, plug in the values into the formula:

Confidence Interval = 24.8 ± (1.645 * 6.9 / √(40))

Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size:

SE = 6.9 / √(40)

Calculate the margin of error by multiplying the critical value with the standard error:

Margin of Error = 1.645 * SE

Finally, calculate the confidence interval:

Confidence Interval = 24.8 ± Margin of Error

Perform the calculations to find the lower and upper bounds of the confidence interval:

Lower Bound = 24.8 - Margin of Error

Upper Bound = 24.8 + Margin of Error

The resulting confidence interval is (22.96, 26.64).In this case, the confidence interval (22.96, 26.64) is constructed based on the sample mean of 24.8 and the standard deviation of 6.9.

Option c correctly states that Kat can be 90% confident that the true mean number of eggs chickens from this farm lay falls within the interval (22.96, 26.64). This means that if we were to repeat the sampling process multiple times and construct confidence intervals, about 90% of those intervals would contain the true mean.

Options a and b are incorrect because they do not accurately describe the interpretation of a confidence interval. Option d is also incorrect as it mentions "repeated sampling" but does not accurately convey the meaning of the confidence interval capturing the true mean.

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Answer:

Therefore, the value of Lucie's house after 7 years would be approximately £214,417.80, rounded to four significant figures.

Step-by-step explanation:

To calculate the value of Lucie's house after 7 years with an annual increase of 1.05%, we can use the formula for compound interest:

Final Value = Initial Value × (1 + Growth Rate)^Number of Years

In this case, the initial value of the house is £200,000, the growth rate is 1.05% (or 0.0105 as a decimal), and the number of years is 7.

Calculating the final value:

Final Value = £200,000 × (1 + 0.0105)^7

Final Value = £200,000 × (1.0105)^7

Final Value ≈ £200,000 × 1.072089

Final Value ≈ £214,417.80

Therefore, the value of Lucie's house after 7 years would be approximately £214,417.80, rounded to four significant figures.

Answer:

Therefore, the value of Lucie's house after 7 years would be approximately £214,417.80, rounded to four significant figures.

Step-by-step explanation:

When countries such as Kenya and Uganda shift from low-impact subsistence lifestyles to high-impact consumer economies, environmentalists are concerned about the potential negative impacts on natural resources and ecosystems.

The shift to high-impact consumer economies often leads to increased industrialization, urbanization, and resource exploitation, which can have detrimental effects on the environment. This includes deforestation, habitat destruction, water pollution, air pollution, and increased greenhouse gas emissions.

As countries pursue economic growth and development, there is a higher demand for energy, raw materials, and natural resources, resulting in unsustainable practices that can deplete natural resources and degrade ecosystems.

This can lead to loss of biodiversity, disruption of ecosystems, and further exacerbation of climate change. Environmentalists advocate for sustainable development practices that balance equation with environmental protection to mitigate these concerns and promote long-term ecological sustainability.

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According to the Law of Cosines, The length of side j in triangle JKL is approximately 12.7 inches (rounded to the nearest 10th of an inch).

To find the length of side j in triangle JKL, we can use the Law of Cosines. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides, minus twice the product of their lengths and the cosine of the included angle.

Applying the Law of Cosines, we have:

j² = k² + l² - 2kl × cos(J)

Substituting the given values, we get:

j² = (4.4)² + (8.6)² - 2(4.4)(8.6) × cos(129°)

Calculating this expression, we find j ≈ 12.7 inches (rounded to the nearest 10th of an inch).

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As an AI language model, I don't have a previous or current company. However, many companies present their triple bottom line performance through sustainability reports, integrated annual reports, or dedicated sections on their websites.

Companies that embrace the concept of the triple bottom line often provide detailed reports or disclosures to showcase their performance in economic, social, and environmental aspects. These reports typically include key metrics, goals, and initiatives related to each dimension.

In their reports, companies may highlight their economic performance by showcasing financial indicators such as revenue, profit, and return on investment. They may also discuss their efforts to create economic value and contribute to the local economy through job creation or supplier relationships.

For the social dimension, companies may outline their initiatives related to employee welfare, diversity and inclusion, community engagement, and philanthropic activities. They may provide data on employee satisfaction, workforce diversity, community development projects, and partnerships with nonprofit organizations.

Regarding the environmental dimension, companies may disclose their environmental impact, resource management practices, energy efficiency initiatives, waste reduction efforts, and carbon footprint. They may also discuss their commitment to sustainable sourcing, renewable energy, and environmental conservation.

These presentations of the triple bottom line aim to provide stakeholders with a comprehensive understanding of a company's performance and its commitment to sustainable and responsible business practices.

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Answer:  25

Step-by-step explanation:

Triangle proportionality theorem only work for the sides of the triangle.

You can use the fact that the 2 triangles are similar.

Given:

DG = 15

GH=20

DE = 32

GF ~ GF+DG         Using entire sides of the triangle

GH ~ DE

So I can say:

[tex]\frac{GF}{GF+DG} = \frac{GH}{DE}[/tex]                        >Substitute given

[tex]\frac{GF}{GF+15} = \frac{20}{32}[/tex]                           >Reduce

[tex]\frac{GF}{GF+15} = \frac{5}{8}[/tex]                             >Cross Multiply

8(GF) =  5(GF +15)                >Distribute

8(GF) =  5(GF) +75                >Simplify

3(GF) = 75

GF = 25

The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. The probability that her trip will take longer than 80 minutes is 20 minutes.

To determine the probability that the student's trip will take longer than 80 minutes, we need to calculate the area under the probability density function (PDF) curve for the given uniform distribution.

Hence, the probability that the trip will take longer than 80 minutes, we need to calculate the proportion of the total range that lies beyond 80 minutes.

The total range is 90 - 40 = 50 minutes.

The portion of the range beyond 80 minutes is 90 - 80 = 10 minutes.

Therefore, the probability that the trip will take longer than 80 minutes is:

P(trip longer than 80 minutes) = (portion beyond 80 minutes) / (total range)

P(trip longer than 80 minutes) = 10 / 50 = 0.2 or 20%

So, the correct answer is 20.

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Autumn's physiological response, characterized by her increased heart rate, sweaty hands, and flushed cheeks, indicates that her sympathetic nervous system has been activated.

Autumn's physiological response, such as an increased heart rate, sweaty hands, and flushed cheeks, is a typical manifestation of the fight-or-flight response, which is controlled by the sympathetic nervous system. In this situation, Autumn's body is reacting to a perceived threat or a stressful stimulus, which in this case is the presence of the boy she has a crush on.

When the sympathetic nervous system is activated, it triggers the release of stress hormones like adrenaline, which leads to various physiological changes in the body. These changes include increased heart rate, dilation of blood vessels, increased blood flow to the muscles, and sweating, all of which prepare the body for action in response to a perceived threat. This response is part of the body's automatic reaction to stressful or arousing situations and helps to mobilize the body's resources to deal with the perceived threat or challenge.

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The command "chage -M 60 -W 10 jsmith" sets the password for the user "jsmith" to expire after 60 days and provides a warning 10 days before it expires.

The command "chage" is used in Unix-like operating systems to modify user password aging policies. In this case, the "-M" option sets the maximum number of days the password is valid, which is 60 in this command. This means that after 60 days, the user "jsmith" will be required to change their password. The "-W" option sets the number of days before the password expiration when the user will receive a warning message, which is 10 days in this command.

Therefore, 10 days before the password expires, "jsmith" will be notified to change their password. This command ensures that the password for the user "jsmith" will expire after 60 days and provides a warning 10 days prior to the expiration.

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The value of function f (3) is,

⇒ f (3) = - 3/2

We have to given that;

The graph of y = f(x) is shown below.

Two points on the line are (4, 0) and (0, -4).

Since, The equation of line passes through the points (4, 0) and (0, -4).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 6 - 0)) / (0 - 4)

m = - 6 / - 4

m = 3/2

Thus, The equation of line with slope 3/2 is,

⇒ y - 0 = 3/2 (x - 4)

⇒ y = 3/2x - 6

Therefore, The equation of line passes through the points (4, 0) and (0, -4). will be;

⇒ f (x) = 3/2x - 6

Hence, The value of f (3) is,

⇒ f (x) = 3/2x - 6

⇒ f (3) = 3/2 × 3 - 6

⇒ f (3) = 9/2 - 6

⇒ f (3) = - 3/2

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A key problem faced by poorer inner-city neighborhoods in America due to their geographical position is a lack of quality food options.

One of the significant challenges faced by poorer inner-city neighborhoods in America is the limited availability of quality food options, commonly referred to as "food deserts." Food deserts are areas where residents have limited access to fresh, nutritious, and affordable food. These neighborhoods often lack grocery stores, farmers markets, and other sources of healthy food, leaving residents with few choices but to rely on convenience stores and fast food outlets that predominantly offer processed and unhealthy food options.

The geographical positioning of these neighborhoods plays a crucial role in this interest. Many low-income inner-city neighborhoods are located in areas that are underserved by grocery stores and supermarkets.

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Two-tailed because there is no predicted direction of the difference. The correct answer is D.

In hypothesis testing, a one-tailed test is used when the researcher has a specific prediction about the direction of the effect. They expect the results to be either greater than or less than a certain value. However, in this scenario, the researcher simply wants to investigate whether the new type of exercise improves people's health without any specific directional prediction.

A two-tailed test is appropriate when the researcher wants to determine if there is a significant difference between the groups being compared, but without specifying the direction of the difference. In this case, the researcher wants to examine if the new exercise has any effect on health, whether it improves or worsens it. Therefore, a two-tailed test is suitable as it allows for the possibility of observing a significant difference in either direction.

Therefore, considering these factors, the researcher should conduct a two-tailed test to assess the potential impact of the new exercise on people's health. The correct answer is D.

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The volume of the right prism with a base area of 10 square feet and a height of 6 feet is 60 cubic feet.

A prism is a polyhedron that has a base and a top face that are the same in size and shape, with sides connecting them that are rectangles in a right prism.

A right prism is a prism in which all of the side faces are perpendicular to the base.

Therefore, the height of the right prism is perpendicular to the base as well.

A right prism has a volume equal to the product of the base area and the height.

This formula can be represented as:

V = Bh

Here, B represents the area of the base, and h represents the height.

The volume of the right prism can be found by multiplying the area of the base by the height of the prism, according to the formula:

V = Bh.

In this problem, the area of the base of the prism is given to be 10 square feet.

The height of the prism is 6 feet.

We can simply substitute these values into the formula to obtain the volume of the right prism as follows:

V = BhV

   = 10 × 6V

   = 60

Therefore, the volume of the right prism is 60 cubic feet.

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Answer:

The mass of raisins to the mass of butter can be expressed in simplified ratio form as X:Y, where X represents the mass of raisins and Y represents the mass of butter.

To determine the reasonable equation for the least-squares regression line for the predicted highway MPG based on weight, we need to consider the scatterplot. In a scatterplot, the least-squares regression line represents the best-fit line that minimizes the distance between the observed data points and the line.

Looking at the given equation options, we can eliminate those with a positive coefficient for weight (since weight is typically expected to negatively impact fuel efficiency) and those with a constant term significantly different from the observed data points.

Out of the remaining options, the equation "predicted highway mpg = 32.3 – 0.0067 (weight)" seems the most reasonable. This equation suggests that as the weight of the car increases, the predicted highway MPG decreases.

The equation of a regression line is typically written as y = mx + b, where y represents the dependent variable, x represents the independent variable, m represents the slope of the line, and b represents the y-intercept.

The slope, m, represents the rate of change of y with respect to x, while the y-intercept, b, represents the predicted value of y when x is zero.

The constant term (32.3) aligns reasonably with the observed data points, and the negative coefficient for weight reflects the expected negative relationship between weight and fuel efficiency.

Therefore, the equation "predicted highway mpg = 32.3 – 0.0067 (weight)" is a reasonable description of the least-squares regression line for the predicted highway MPG based on weight.

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Answer:

Step-by-step explanation:

You want to know the price per bushel for wheat, corn, and rye, given the sales ...

Using x, y, and z for price per bushel of wheat, corn, and rye, respectively, the given sales tell us ...

The easiest way to solve a system of equations like this is to make use of the matrix manipulation capabilities of a calculator. The attached calculator display shows the reduction of the augmented matrix of coefficients to "reduced row-echelon form". That puts the solution in the last column:

  x = y = 3.61, z = 1.91

The price per bushel for wheat and corn is the same: $3.61; the price per bushel for rye is $1.91.

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Additional comment

The second attachment shows a solution using a graphing calculator. In this solution, an expression for z based on the first equation is used in the remaining two equations, which then tell us the values of x and y.

If you add all of the equations, you get 10x +10y +10z = 91.30, which gives you ...

  x + y + z = 9.13

This can be solved for any variable you may want to substitute into any pair of the equations. This approach avoids any messy fractions.

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Answer:

School A: 850 + 45t

School B: 1000 + 35t

After 15 years, both school has same strength and the total students in both school is 1525.

Step-by-step explanation:

                                      Current strength = 850 students.

   New admission of students each year = 45 students

   New admission of students in 't' years = 45*t = 45t

To find the total students after 't' years, add the current strength with 45t.

   Total strength of the school A after 't' years = 850 + 45t

                                      Current strength = 1000 students.

   New admission of students each year = 35 students

   New admission of students in 't' years = 35*t = 35t

To find the total students after 't' years, add the current strength with 35t.

   Total strength of the school B after 't' years = 850 + 35t

It is given that, the number of students are same in both schools after 't' years.

         Strength of School A = Strength of School B

                850 + 45t             = 1000 + 35t

                                      45t = 1000 + 35t - 850

                                     45t  = 1000 - 850 + 35t

                                     45t  = 150 + 35t

                              45t - 35t = 150

                                     10t   = 150

                                        t    = 150 ÷ 10

                                       t = 15

Strength of School A = 850 + 45 *15

                                   = 850 + 675

                                   = 1525

Strenght of school B = 1000 + 35*15

                                  = 1000 + 525

                                  = 1525