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

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