Question

A grocer bought 300 pounds of bananas at 30 cents per pound. Experience at this store indicates that, as a result of aging, 30% of the bananas are sold at 80% of cost and another 10% are discarded. At what price per pound must the top-quality bananas be sold so that the total proceeds will result in a 20% markup on selling price? Round up to the nearest penny.
a. $0.51
b. $0.38
c. $0.44
d. $0.30

Answer 1

cost price = 30cents per pound for a total of 9000 cents

30% of 300 pounds sold at .8 of 30 cents, or 24 cents per pound
----> 90 pounds sold for 2160 cents
10% of 300 pounds sold at 0
---> 30 pounds sold for 0 cents
leaving 60% or 180 pounds sold at x cents per pound for a return of
180x cents
selling price = 2160+0+180x = 180x + 2160
profit = 180x+2160 - 9000
= 180x - 6840

(180x-6840)/(180x+2160) = 1/5
900x - 34200 = 180x + 2160
720x = 36360
x = 50.5 cents or 51 cents

check:
90 lbs sold at 24 cents = 2160
30 lbs sold at 0 cents = 0
180 lbs sold at 50.5 = 9090
profit = (2160+9090) - 9000 = 2250

markup based on Selling price = 2250/(2160+9090) = .20