South African Mathematics Olympiad

Question

Steve was sorting 1,000 eggs into sizes. He got paid 20 cents for each egg that he sorted. For each egg that he broke while sorting he did not get paid and had to pay his employer R1. Steve was paid R176. How many eggs did Steve break?

Accepted Answer

Suppose Steve breaks n eggs, so 1,000 - n eggs are unbroken. He receives R0.20 (1,000 - n), but has to repay R1 n. Thus 0.2(1,000 - n) - n = 176, giving 200 - 1.2n = 176, so 1.2n = 200 - 176 = 24 and n = 20.