Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.9 AIME Prove it South Africa

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?

Solution

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

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