1950 AMC 12 Problem 31
Attempt Problem 31 of the 1950 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1950 AMC 12 solutions, or check the answer key.
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31.
John ordered pairs of black socks and some additional pairs of blue socks. The price of the black socks per pair was twice that of the blue. When the order was filled, it was found that the number of pairs of the two colors had been interchanged. This increased the bill by The ratio of the number of pairs of black socks to the number of pairs of blue socks in the original order was:
Answer: C
Small hint:
Let a blue pair cost and let be the original number of blue pairs
Big hint:
Compare the original bill with the interchanged bill
Solution:
Let a blue pair cost so a black pair costs and let be the original number of blue pairs. The original bill is After the quantities are interchanged, the bill is The latter is greater, so Thus and the original black-to-blue ratio is
Thus, the correct answer is C.