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. $0.30
Question
Answer:
We are only interested in price per pound (the unit price), so we can figure the whole problem considering only 1 lb of bananas.Let p represent the selling price of the top-quality bananas (per pound). The revenue from the sale of those will be
p*(1 -0.30 -0.10) = 0.60p
The revenue from the sale of aged bananas will be
0.30*(0.80*$0.30) = $0.072
Then the total revenue is
(revenue from top quality bananas) +(revenue from aged bananas)
total revenue = 0.60p +0.072
The cost of the bananas is $0.30 (per pound).
Then the proceeds are
proceeds = (total revenue) - cost
And the problem tells us we want the proceeds to be 20% of the total revenue.
(total revenue) -cost = 0.20*(total revenue)
0.80*(total revenue) = cost
0.80*(0.60p +0.072) = 0.30
0.60p = (0.30/0.80) -0.072
p = 0.303/0.60 = 0.505
The best choice for the selling price of top quality bananas is ...
a. $0.51
solved
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10 months ago
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