Question

An electric guitar costs $830, with a $225 full-replacement warranty. If the manufacturer sells 532,475 warranties and has to honor 12% of them, how much profit did the manufacturer gain from the warranties?

Answer 1

1. Count 12% of 532,475:

532,475 - 100%

x - 12%

Use proportion to find x:

$\dfrac{532,475}{x}=\dfrac{100}{12},\\ \\x=\dfrac{532,475\cdot 12}{100}=63,897.$

This means that 63,897 electric guitars were sold with full-replacement warranty and 532,475-63,897=468,578 electric guitars were sold without full-replacement warranty.

2. If the manufacturer sells 468,578 electric guitars without full-replacement warranty, then he gain profit

$225·468,578=$105,430,050

from the warranties.

Answer: $105,430,050

Answer 2

If 532,475 warranties were given, it means that 532,475 warranties were sold. The gross profit should be, 532,475 * $830 = $441954250. But then, this would still be subtracted with 12% of the warranties since they gave it back to the customers. Hence,

Profit = $441954250 – 0.12(532,475)($225)

Profit = $427,577,425