High School

Mr. Green uses a linear function to estimate how installing solar panels on the roof of his house will reduce his electric bill. Mr. Green does not have any solar panels yet, and his electric bill is \$133 per month on average. For each 100 square feet of solar panels he installs, Mr. Green's monthly electric bill will decrease by \$13.50. How many square feet of solar panels must Mr. Green install to reduce his monthly electric bill to \$25?

a) 800
b) 850
c) 900
d) 950

Answer :

Final answer:

Mr. Green needs to install 800 square feet of solar panels to reduce his electric bill to $25 per month, by setting up and solving a linear equation based on the rate of decrease per 100 square feet of panels.

Explanation:

Mr. Green wants to reduce his monthly electric bill from $133 to $25 by installing solar panels. The reduction in the bill is proportional to the number of solar panels installed, with each 100 square feet resulting in a $13.50 decrease. To find out how many square feet he must install, we can set up a linear equation:

Let x be the total square feet of solar panels Mr. Green needs to install.

The decrease in the electric bill for every 100 square feet of solar panels is $13.50, so the decrease for x square feet would be $13.50/100 times x or 0.135x.

The original bill is $133, and he wants to reduce it to $25, so the total decrease he seeks is $133 - $25, which equates to $108. We can now set up the equation 0.135x = $108 and solve for x:

  1. Divide both sides by 0.135 to isolate x.
  2. x = $108 / 0.135
  3. x = 800

Therefore, Mr. Green must install 800 square feet of solar panels to reduce his monthly electric bill to $25.

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