2470.62 – Solar Panel

If a certain type of solar panel were to be sold for $\text{\textdollar}x$ , the seller would take a 15 percent loss based on materials required to produce it. If the same solar panel were sold for $\text{\textdollar}y$ , the seller instead would make a 15 percent profit based on cost. What is the ratio of $x$ to $y$ ?

Solution

If $c$ is the cost of producing the panel, then we know that $x=0.85c$ and $y=1.15c$ . Therefore:

$\frac{x}{y}=\frac{0.85c}{1.15c}=\frac{0.85}{1.15}=\frac{17}{23}.$

The ratio of $x$ to $y$ is 17 to 23, or about 3 to 4.

(Is this problem for real, or is it just a cheap way of having students to do a lot of work?)