Bunuel wrote:
If each of three grocery stores receives 1/4 of a farmer’s potato crop, a farmer’s market receives 1/3 of the remaining, and a local fast food restaurant receives the remaining 200 pounds, how many pounds of potatoes were in the farmer’s crop?
A. 300
B. 400
C. 900
D. 1,200
E. 1,400
(1) Each of 3 grocery stores gets \(\frac{1}{4}\) of the potato crop
\(3*\frac{1}{4}=\frac{3}{4}\) is gone,
and \(\frac{1}{4}\) remains
(2) \(\frac{1}{3}\) of the remaining \(\frac{1}{4}\) goes to a farmer's market
\((\frac{1}{3}*\frac{1}{4})=\frac{1}{12}\) more is gone
FRACTION GONE:\((\frac{3}{4}+\frac{1}{12})=\frac{10}{12}\) gone, and
FRACTION LEFT
\((1-\frac{10}{12})=(\frac{12}{12}-\frac{10}{12})=\frac{2}{12}=\frac{1}{6}\) remains
(3) How many pounds of potatoes, P, were there to begin with?
200 lbs of potatoes remain
\(\frac{1}{6}\) of \(P\) remains
\(200=\frac{1}{6}P\)
\(P=1,200\)
Answer D
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