0.30P+0.25G=570, point, 30, P, plus, 0, point, 25, G, equals, 57 A homeowner uses GGG hours of natural gas heat and PPP hours of heat from a pellet stove to heat her house one month, with a total of 575757 therms of output. How many therms per hour does the pellet stove output?

Answer:

this is a SAT college question that involves solving a system of equations with two variables, P and G. P represents the number of hours of heat from a pellet stove, and G represents the number of hours of natural gas heat. The equation 0.30P+0.25G=570 means that the total cost of heating for one month is 570 dollars, where 0.30 dollars is the cost per hour of pellet stove heat and 0.25 dollars is the cost per hour of natural gas heat.

The question also gives another equation: P+G=57, which means that the total number of hours of heating for one month is 57 hours.

To find how many therms per hour does the pellet stove output, we need to solve this system of equations for P and G, and then use another formula that relates therms to kilowatt-hours (kWh).

one therm (US) is equal to 29.3001111 kWh.

We can use substitution or elimination method to solve the system of equations:

Using substitution:

P+G=57 P=57-G

Substitute P into the first equation:

0.30(57-G)+0.25G=570 17.1-0.30G+0.25G=570 -0.05G=-552.9 G=11058

Plug G into either equation to find P:

P+11058=57 P=-11001

Using elimination:

Multiply both sides of the second equation by -0.25:

P+G=57 -0.25P-0.25G=-14.25

Add both equations together:

(0.30P-0.25P)+(0.25G-0.25G)=570-14.25 0.05P=55575 P=-111015

Plug P into either equation to find G:

-111015+G=57 G=11072

We can see that both methods give us the same values for P and G.

Now we can use these values to find how many therms per hour does the pellet stove output.

We know that one therm (US) is equal to 29.3001111 kWh, so we can write:

Therms per hour = kWh per hour / 293001111

We also know that kWh per hour = Cost per hour / Cost per kWh.

in February 2023, the average cost per kWh in Kentucky was $0.11.

So we can write:

Therms per hour = (Cost per hour / $011) / 293001111

For pellet stove heat, we have:

Therms per hour = ($030 / $011) / 293001111 Therms per hour = ~0000036

Therefore, the pellet stove outputs about 0000036 therms per hour.

Explanation:

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