2014 AMC 12A Problem 4 — Solution | LIVE by Po-Shen Loh

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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 $a$ cows give $b$ gallons of milk in $c$ days. At this rate, how many gallons of milk will $d$ cows give in $e$ days?

$\dfrac{bde}{ac}$

$\dfrac{ac}{bde}$

$\dfrac{abde}{c}$

$\dfrac{bcde}{a}$

$\dfrac{abc}{de}$

Answer: A

Concepts:rate ratio and proportion

Difficulty rating: 1200

Solution:

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

So $d$ cows over $e$ days produce $\dfrac{b}{ac}\cdot d\cdot e=\dfrac{bde}{ac}$ gallons.

Thus, the correct answer is A.

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