2014 AMC 10A Problem 6

Question

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}

Find the production rate per cow per day

Scale by

d

cows and

e

days

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.

Problem 6 in other years