2014 AMC 10A Problem 6 — Solution | LIVE by Po-Shen Loh

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2014 AMC 10A Problem 6

Below is the professionally curated solution for Problem 6 of the 2014 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 10A solutions, or check the answer key.

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Concepts:ratio and proportion rate

Difficulty rating: 870

6.

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?

$\dfrac{bde}{ac}$

$\dfrac{ac}{bde}$

$\dfrac{abde}{c}$

$\dfrac{bcde}{a}$

$\dfrac{abc}{de}$

Solution:

We have to multiply $b$ by $\dfrac{d}{a}$ to account for the new number of cows.

We then have to multiply by $\dfrac{e}{c}$ to account for the new time that we have.

This gives us a final answer of $b \cdot \dfrac{d}{a} \cdot \dfrac{e}{c} = \dfrac{bde}{ac}.$

Thus, A is the correct answer.

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