2470.62 – Solar Panel

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

Solution

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

xy=0.85c1.15c=0.851.15=1723\dfrac{x}{y}=\dfrac{0.85c}{1.15c}=\dfrac{0.85}{1.15}=\dfrac{17}{23}

The ratio of xx to yy 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?)