sandy wrote:

If each of three grocery stores receives of a farmer’s potato crop, a farmer’s market receives 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

e can let n = the total number of pounds of potatoes in the farmer’s crop. Note that 3/4 of his crop went to the grocery stores, leaving 1/4 of the crop remaining. We know that 1/3 of this remaining 1/4 went to the farmer’s market, and the remaining 200 pounds went to the fast food restaurant. We can create the equation:

n = 3(1/4)n + 1/3(1/4)n + 200

n = (3/4)n +(1/12)n + 200

12n = 9n + n + 2400

2n = 2400

n = 1200

Alternate Solution:

We know that 3/4 of the crop went to grocery stores, and (1/3)(1/4) = 1/12 of the crop went to the farmer’s market. Thus, we see that 3/4 + 1/12 = 9/12 + 1/12 = 10/12 of the crop went to these endeavors, leaving 2/12 = 1/6 of the crop, which is equal to 200 pounds, to go to the fast food restaurant. Thus, if we let n = the number of pounds of potatoes in the crop, we see that:

(1/6)n = 200

n = 1200

Answer: D

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