2014 AMC 12A Problems/Problem 4
Problem
Suppose that cows give
gallons of milk in
days. At this rate, how many gallons of milk will
cows give in
days?
$\textbf{(A)}\ \frac{bde}{ac}\qquad\textbf{(B)}\ \frac{ac}{bde}\qquad\textbf{(C)}\ \frac{abde}{c}\qquad\textbf{(D)}}\ \frac{bcde}{a}\qquad\textbf{(E)}\ \frac{abc}{de}$ (Error compiling LaTeX. Unknown error_msg)
Solution 1
We need to multiply by
for the new cows and
for the new time, so the answer is
, or
.
(Solution by ahaanomegas)
Solution 2
We see that the the amount of cows is inversely proportional to the amount of days and directly proportional to the gallons of milk. So our constant is .
Let be the answer to the question. We have