Bunuel wrote:
A fruit seller bought 2000 quarts of berries at 80 cents per quart. If 1/4 of the berries become too ripe for sale, what should be the selling price per quart of the remainder so that the gross profit will be 20 percent of the total cost?
(A) $0.25
(B) $0.80
(C) $1.00
(D) $1.10
(E) $1.28
Profit = TR - TC,
AND TR = TC + Profit
Because we can find both TC and profit pretty easily, find what TR must be and divide by number of quarts sold to get sell price per quart
TC, Profit, TRTR = TC + Profit
TR = (# quarts sold)*(Price, P, per quart)
Find Total Cost:
2,000 quarts at $0.80 per quart
TC = (2,000 * $0.80) = $1,600
Find Profit: 20 percent of TC
Profit= (.20 * $1,600) = $320
TR = $320 + $1,600 = $1,920
Sell price per quart?Find sell price from the other TR formula
TR =$1,920= (# qrts sold)*(Price, P, per qrt)
How many quarts sold?
(2,000 - 500) = 1,500 quarts sold
At what sell price per item, P?
TR= (# of items)*(sell price per item,P)
\($1,920 =1,500P\)
\(P =\frac{$1,920}{1,500}=$1.28\)ANSWER E
Once we have
\($1,920 =1,500P\)
there is no need to calculate exactly.
Answers A, B, and C are too small.
Answer C, e.g., $1.00:
1,500*$1.00 = $1,500. Not close to $1,920
Answer D, mental math eliminates. Split $1.10 into $1 and $0.10
1,500 * $1 = $1,500
1,500 * $0.10 = $150
= $1,650 total
By POE, ANSWER E *Faster: Profit is 20 percent of the total cost = 20 percent more than total cost= TR:
($1,600 * 1.2) = $1,920 = TR
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