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