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29 Dec 2023, 10:35
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C
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Difficulty:
45%
(medium)
Question Stats:
80% (03:15) correct
20%
(03:28)
wrong
based on 850
sessions
History
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A certain store purchased grills for $50 each and lawn chairs for $5 each and then sold each grill and each chair. The store's gross profit on each grill was 30 percent of its purchase price, and the store's gross profit on each chair was 50 percent of its purchase price. If the store sold 5 times as many chairs as grills and if the store's total gross profit on the grills and chairs was $550, what was the store's total revenue from the sale of the grills and chairs?
A. $1,530
B. $1,800
C. $2,050
D. $2,100
E. $2,360
Screenshot 2023-12-29 230227.png [ 127.18 KiB | Viewed 16562 times ]
A. $1,530
B. $1,800
C. $2,050
D. $2,100
E. $2,360
Attachment:
Screenshot 2023-12-29 230227.png [ 127.18 KiB | Viewed 16562 times ]
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29 Dec 2023, 10:51
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gmatophobia
Let there be x grills sold, then 5x chairs are sold.
Profit on each grill: 30% of 50 or $15
Profit on each chair: 50% of 5 or $2.5
Total profit = 15*x + 2.5*5x = 27.5x = 550
x = 20
Thus revenue generated = cost + profit
50*20 + 5*100 + 550 = 1500 + 550 = $2050
C
If we were to give slightly lucrative wrong options, 1500 would surely be an option.
General Discussion
01 Jan 2024, 06:16
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Let's denote the number of grills purchased as = G
and the number of lawn chairs purchased as = C
Given:
Purchase price for each grill = $50
Purchase price for each lawn chair = $5
The store's gross profit on each grill is 30% of its purchase price, so the profit per grill is 0.30 *50 = $15.
The store's gross profit on each chair is 50% of its purchase price, so the profit per chair is 0.50 * 5 = $2.50.
Now, the store sold 5 times as many chairs as grills, so
C=5G.
The total gross profit on grills is 0.3*50 = $15
on chairs is 0.5*5 = $2.50
and the total gross profit on both is given as $550.
So, we can set up the equation:
15G+2.50C=550
Now, substitute
C=5G into the equation:
15G+2.50(5G)=550
Solve for G
G=20
C=5G=5×20=100
The total revenue from the sale of grills is 20 *(50 + 15) = 20 * 65 = $1300.
The total revenue from the sale of chairs is 100 * (5 + 2.50) = 100 * 7.50 = $750.
Therefore, the store's total revenue from the sale of grills and chairs is $1300 + $750 = $2050.
and the number of lawn chairs purchased as = C
Given:
Purchase price for each grill = $50
Purchase price for each lawn chair = $5
The store's gross profit on each grill is 30% of its purchase price, so the profit per grill is 0.30 *50 = $15.
The store's gross profit on each chair is 50% of its purchase price, so the profit per chair is 0.50 * 5 = $2.50.
Now, the store sold 5 times as many chairs as grills, so
C=5G.
The total gross profit on grills is 0.3*50 = $15
on chairs is 0.5*5 = $2.50
and the total gross profit on both is given as $550.
So, we can set up the equation:
15G+2.50C=550
Now, substitute
C=5G into the equation:
15G+2.50(5G)=550
Solve for G
G=20
C=5G=5×20=100
The total revenue from the sale of grills is 20 *(50 + 15) = 20 * 65 = $1300.
The total revenue from the sale of chairs is 100 * (5 + 2.50) = 100 * 7.50 = $750.
Therefore, the store's total revenue from the sale of grills and chairs is $1300 + $750 = $2050.
