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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

Respuesta :

sqdancefan
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

i feel like its A but i am dumb

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