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?

Question

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?

Bytelearn · Accepted Answer

Denoting the Output of the Pellet Stove: Let's denote the number of therms per hour the pellet stove outputs as P. We are given the equation 0.30P + 0.25G = 57, where G is the number of hours of natural gas heat used. We want to find the value of P, which represents the therms per hour output of the pellet stove.Isolating P in the Equation: To find P, we need to isolate it on one side of the equation. However, we have two variables in the equation, P and G. Since we are only asked to find P, we can treat G as a constant or ignore it for now, as we are not asked to find its value.Rewriting the Equation: We can rewrite the equation to solve for P: 0.30P = 57 - 0.25G.Dividing Both Sides of the Equation: Now, we divide both sides of the equation by 0.30 to solve for P: P = (57 - 0.25G) / 0.30.Expressing P in Terms of G: We notice that we cannot solve for P directly because we do not have the value of G. However, since we are only asked for the therms per hour output of the pellet stove (P), we can express P in terms of G: P = (57/0.30) - (0.25G/0.30).Simplifying the Equation: Simplify the equation: P = 190 - (5/6)G.Answering the Question Prompt: We realize that we cannot find a numerical value for P without knowing G. The question prompt asks for the therms per hour output of the pellet stove, which is represented by P in the equation. Therefore, the answer to the question prompt is that the pellet stove outputs 0.30 therms per hour, as indicated by the coefficient of P in the original equation.

$0.30 P+0.25 G=57$ $\newline$ 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?

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0.30P+0.25G=57 0.30 P+0.25 G=57 0.30P+0.25G=57\newlineA homeowner uses G G G hours of natural gas heat and P P P 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?

$0.30 P+0.25 G=57$ $\newline$ 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?