2014 AMC 12A Problem 4

Attempt Problem 4 of the 2014 AMC 12A 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 2014 AMC 12A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

4.

Suppose that aa cows give bb gallons of milk in cc days. At this rate, how many gallons of milk will dd cows give in ee days?
bdeac\dfrac{bde}{ac}
acbde\dfrac{ac}{bde}
abdec\dfrac{abde}{c}
bcdea\dfrac{bcde}{a}
abcde\dfrac{abc}{de}
Answer: A
Concepts:rateratio and proportion
Small hint:
Find how much milk one cow gives in one day
Big hint:
One cow gives bac\dfrac{b}{ac} gallons per day; scale by dd cows and ee days
Solution:
The rate is bac\dfrac{b}{ac} gallons per cow per day.
So dd cows over ee days produce bac⋅d⋅e=bdeac\dfrac{b}{ac}\cdot d\cdot e=\dfrac{bde}{ac} gallons.
Thus, the correct answer is A.
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