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
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
To solve this problem, we need to calculate the total cost of the bananas, the total selling price, and then determine the selling price per pound for the top-quality bananas.
First, let's calculate the total cost of all the bananas purchased:
Total Cost = Amount Bought × Cost per pound
Total Cost = 300 pounds × $0.30/pound = $90
Next, we need to calculate the selling price for the bananas sold at 80% of cost:
Bananas Sold at 80% of Cost = 30% of Total Bought
Bananas Sold at 80% of Cost = 0.30 × 300 pounds = 90 pounds
Selling Price for 80% of Cost Bananas = 80% of Cost × Cost per pound
Selling Price for 80% of Cost Bananas = 0.80 × $0.30/pound = $0.24/pound
Now, let's calculate the weight of the bananas that are discarded:
Bananas Discarded = 10% of Total Bought
Bananas Discarded = 0.10 × 300 pounds = 30 pounds
Now, we can find the weight of the top-quality bananas:
Top-Quality Bananas = Total Bought - Bananas Sold at 80% - Bananas Discarded
Top-Quality Bananas = 300 pounds - 90 pounds - 30 pounds = 180 pounds
Next, we need to determine the total selling price for all the bananas sold:
Total Selling Price = Selling Price for 80% of Cost Bananas × Bananas Sold at 80% of Cost + Selling Price for Top-Quality Bananas × Top-Quality Bananas
Since we want to achieve a 20% markup on the selling price, the total selling price must be 120% of the total cost:
Total Selling Price = 1.20 × Total Cost
Now, let's rearrange the equation to solve for the Selling Price for Top-Quality Bananas:
Selling Price for Top-Quality Bananas = (Total Selling Price - Selling Price for 80% of Cost Bananas × Bananas Sold at 80% of Cost) ÷ Top-Quality Bananas
Substituting the values we have:
Selling Price for Top-Quality Bananas = (1.20 × $90 - $0.24/pound × 90 pounds) ÷ 180 pounds
Calculating this expression, we find:
Selling Price for Top-Quality Bananas = $1.47/pound
Rounding up to the nearest penny, we get:
Selling Price for Top-Quality Bananas ≈ $1.48/pound
Therefore, the correct option is d. $0.30