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0.30 P+0.25 G=57
A homeowner uses G hours of natural gas heat and P hours of heat from a pellet stove to heat her house one month, with a total of 57 therms of output. How many therms per hour does the pellet stove output?
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$0.30 P+0.25 G=57$ $\newline$ A homeowner uses $G$ hours of natural gas heat and $P$ hours of heat from a pellet stove to heat her house one month, with a total of $57$ therms of output. How many therms per hour does the pellet stove output? $\newline$ $\square$

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Write and solve equations for proportional relationships

Full solution

Q.

0.30 P+0.25 G=57

\newline

A homeowner uses

G

hours of natural gas heat and

P

hours of heat from a pellet stove to heat her house one month, with a total of

57

therms of output. How many therms per hour does the pellet stove output?

\newline

\square

Understand given equation: First, we need to understand the equation given: $0.30P + 0.25G = 57$ . This equation represents the total therms of output from both the pellet stove and the natural gas heat. We are asked to find the therms per hour output of the pellet stove, which is represented by the coefficient of $P$ in the equation.
Isolate $P$ in equation: To find the therms per hour output of the pellet stove, we need to isolate $P$ in the equation. However, we are not given the value of $G$ , the hours of natural gas heat used, so we cannot solve for $P$ directly. Instead, we can express the therms per hour output of the pellet stove as the coefficient of $P$ , which is $0.30$ .
Express pellet stove output: The coefficient $0.30$ in front of $P$ represents the therms per hour output of the pellet stove. This means that for every hour the pellet stove is used, it produces $0.30$ therms of heat.

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