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.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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.
Problem 31 in Other Years
1951 AMC 12 · 1952 AMC 12 · 1953 AMC 12 · 1954 AMC 12 · 1955 AMC 12 · 1956 AMC 12 · 1957 AMC 12 · 1958 AMC 12 · 1959 AMC 12 · 1960 AMC 12 · 1961 AMC 12 · 1962 AMC 12 · 1963 AMC 12 · 1964 AMC 12 · 1965 AMC 12 · 1966 AMC 12 · 1967 AMC 12 · 1968 AMC 12 · 1969 AMC 12 · 1970 AMC 12 · 1971 AMC 12 · 1972 AMC 12 · 1973 AMC 12