A shipment of 1,500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived, 2/3 of the heads were sold, each at 25 percent above the cost per head. The following day the rest were sold at a price per head equal to 10 percent less than the price each head sold for the day before. What was the gross profit on this shipment?
A) $100
B) $115
C) $125
D) $130
E) $135
Any useful shortcuts?
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Cabbage shipments
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1,500 heads of cabbage purchased for $600kobel51 wrote:A shipment of 1,500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived, 2/3 of the heads were sold, each at 25 percent above the cost per head. The following day the rest were sold at a price per head equal to 10 percent less than the price each head sold for the day before. What was the gross profit on this shipment?
A) $100
B) $115
C) $125
D) $130
E) $135
So, price per cabbage = 600/1500 = 6/15 = 2/5 = 0.4
So, each cabbage cost $0.40
2/3 of the heads were sold, each at 25 percent above the cost per head.
2/3 of 1500 = 1000. So, 1000 heads we sold.
25% of $0.40 = $0.10. So, the selling price = $0.40 + $0.10 = $0.50
Revenue = (1000)($0.50) = $500
The following day the rest were sold at a price per head equal to 10 percent less than the price each head sold for the day before
There are 500 heads remaining
10% of $0.50 = $0.05. So, the selling price = $0.50 - $0.05 = $0.45
Revenue = (500)($0.45) = $225
TOTAL REVENUE = $500 + $225 = $725
So, gross profit = $725 - $600 = [spoiler]$125 = C[/spoiler]
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Since we need to calculate the profit for the ENTIRE shipment, we can plug in an EASIER VALUE for the number of heads.kobel51 wrote:A shipment of 1,500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived, 2/3 of the heads were sold, each at 25 percent above the cost per head. The following day the rest were sold at a price per head equal to 10 percent less than the price each head sold for the day before. What was the gross profit on this shipment?
A) $100
B) $115
C) $125
D) $130
E) $135
Any useful shortcuts?
Let the number of heads = 3.
Since the cost of the entire shipment is $600, the cost per head = 600/3 = $200.
2/3 of the heads were sold, each at 25 percent above the cost per head:
For these 2 heads, the selling price per head = 200 + (1/4)(200) = 250.
Profit per head = 250 - 200 = 50.
Total profit = 2*50 = 100.
The following day the rest were sold at a price per head equal to 10 percent less than the price each head sold for the day before.
Selling price for the 1 remaining head = 250 - (1/10)(250) = 225.
Profit = 225-200 = 25.
Total profit for all 3 heads = 100+25 = 125.
The correct answer is C.
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We are given that a shipment of 1500 heads of cabbage costs 600 dollars, or 600/1500 = $0.40 per cabbage.kobel51 wrote:A shipment of 1,500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived, 2/3 of the heads were sold, each at 25 percent above the cost per head. The following day the rest were sold at a price per head equal to 10 percent less than the price each head sold for the day before. What was the gross profit on this shipment?
A) $100
B) $115
C) $125
D) $130
E) $135
We are given that 2/3 x 1500 = 1,000 heads of cabbage sold for 1.25 x $0.40 = $0.50. So, a total of 1,000 x $0.50 = $500 was made on the sale of those heads of cabbage.
The next day, 500 heads of cabbage were sold at a price of 0.9 x $0.50 = $0.45, so a total of 500 x $0.45 = $225 dollars was made on the sale of those heads.
Thus, a total of 500 + 225 = $725 was made.
Thus, profit = 725 - 600 = $125.
Answer: C
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