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Difficulty: HardProfit and Loss

A local cafe owner purchases 5050 pounds of raw coffee beans for $12\$12 per pound. The owner pays a flat shipping fee of $40\$40 for the delivery. During the roasting process, the beans lose 20%20\% of their original weight. If the owner wants to make a 50%50\% profit on the total cost of the order, what must be the selling price per pound of the roasted beans?

  1. $24.00\$24.00Answer
  2. B
    $19.20\$19.20
  3. C
    $32.00\$32.00
  4. D
    $8.00\$8.00

Answer

The required selling price per pound of the roasted beans is $24.00\$24.00.
To find the selling price per pound, we must first determine the total cost. The beans cost 50×$12=$60050 \times \$12 = \$600, plus $40\$40 for shipping, making the total cost $640\$640. A 50%50\% profit on $640\$640 is $320\$320, so the target total revenue is $640+$320=$960\$640 + \$320 = \$960. Next, we must account for the 20%20\% weight loss during roasting. The initial 5050 pounds loses 1010 pounds (0.20×50=100.20 \times 50 = 10), leaving 4040 pounds of sellable roasted beans. Dividing the target revenue by the sellable weight ($960÷40\$960 \div 40) gives exactly $24.00\$24.00 per pound.

Step-by-Step Solution

1
Calculate the total cost of purchasing and shipping the raw coffee beans.
50 lbs×$12/lb=$60050 \text{ lbs} \times \$12/\text{lb} = \$600. Adding the $40\$40 shipping fee gives a total cost of $640\$640.
Profit must be calculated based on the complete overhead and initial investment.
2
Determine the target total revenue required to make a 50%50\% profit.
50%50\% of $640\$640 is $320\$320. The total target revenue is $640+$320=$960\$640 + \$320 = \$960.
The final sales must cover both the initial cost and the desired profit margin.
3
Calculate the final weight of the beans after the roasting process.
The beans lose 20%20\% of their weight. 20%20\% of 50 lbs50 \text{ lbs} is 10 lbs10 \text{ lbs}. The remaining weight is 50−10=40 lbs50 - 10 = 40 \text{ lbs}.
The owner can only sell the roasted beans, so the selling price must be based on the final weight.
4
Calculate the required selling price per pound.
$960÷40 lbs=$24.00 per pound\$960 \div 40 \text{ lbs} = \$24.00 \text{ per pound}.
Dividing the total target revenue by the total sellable pounds yields the unit price.

Key Concept

Calculating multi-step profit requires finding the total investment cost (including overhead), applying the profit percentage to find target revenue, and distributing that target revenue over the final sellable inventory.
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Topics

Profit and Loss

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