2014 AMC 12A Problem 4

Below is the professionally curated solution for Problem 4 of the 2014 AMC 12A, 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.

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Concepts:rateratio and proportion

Difficulty rating: 1200

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}

Solution:

The rate is bac\dfrac{b}{ac} gallons per cow per day.

So dd cows over ee days produce bacde=bdeac\dfrac{b}{ac}\cdot d\cdot e=\dfrac{bde}{ac} gallons.

Thus, the correct answer is A.

Problem 4 in Other Years