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kevincan
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Evercool purchased several portable air conditioners. In J Updated on: 12 Mar 2026, 21:03
Originally posted by kevincan on 12 Mar 2026, 11:48.
Last edited by kevincan on 12 Mar 2026, 21:03, edited 1 time in total.
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C
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65% (hard)

Question Stats:

52% (03:36) correct 48% (03:13) wrong based on 31 sessions

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EverCool purchased several portable air conditioners and sold 4/5 of them in June at the recommended retail price of $800. In July, it sold the remaining units at a 30% discount.

If EverCool’s average profit was $20 per air conditioner, what would the average profit per air conditioner have been if EverCool had sold 9/10 of the units at the recommended retail price and the remaining units at a 30% discount?

A. $36
B. $40
C. $44
D. $48
E. $56
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C
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Evercool purchased several portable air conditioners. In J 12 Mar 2026, 12:24
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EverCool purchased several portable air conditioners and sold 4/5 of them in June at the recommended retail price of $800. In July, it sold the remaining units at a 30% discount.

If EverCool’s average profit was $20 per air conditioner, what would the average profit per air conditioner have been if 9/10 of the units had been sold at the recommended retail price and the remaining units at a 30% discount?

A. $36
B. $40
C. $44
D. $48
E. $56
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Let the total number of units be 10x.

Sold (4/5) of 10x = 8x in June at the retail price of $800.

Revenue = 8x * $800 = $6400x.

(1/5) of 10x = 2x is July is sold at discounted price = 70%*(800) = $560

Revenue = $560*2x = $ 1120x.

Total revenue = $6400x + $1120x = $7520x

Given the average profit is $20. Thus, total profit = $20 * 10x = $200x.

Excluding profit, the revenue = $7520x - $200x = $7320x.

Case 2:

(9/10) of 10x = 9x is sold at Retail price = 9x * $ 800 = $7200x.

(1/10) of 10x = x is sold at $560 = $560x.

Total revenue = $7760x.

Profit in second case = $7760x - $7320x = $440x

Average profit = $440x / 10x = $44.

Option C
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Evercool purchased several portable air conditioners. In J 12 Mar 2026, 12:28
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Five Kudos if anybody can provide a 20 second solution!
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Evercool purchased several portable air conditioners. In J 12 Mar 2026, 12:36
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Thanks Kevin for raising it.

Initial case 80% is sold at 800, while 20% is sold at 560.

Case 2: 90% sold at 800. The additional 10% is from the discounted lot moving to full amount. So, moving you bring the discounted amount back to the total. That’s 240.

So, it brings 10% ( 800-560) = 10%(240) = $24 in excess.

So, the actual profit is $20. Now it’s $20+$24 = $44.
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Evercool purchased several portable air conditioners. In J 13 Mar 2026, 09:57
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Quote:

EverCool purchased several portable air conditioners and sold 4/5 of them in June at the recommended retail price of $800. In July, it sold the remaining units at a 30% discount.

If EverCool’s average profit was $20 per air conditioner, what would the average profit per air conditioner have been if EverCool had sold 9/10 of the units at the recommended retail price and the remaining units at a 30% discount?

A. $36
B. $40
C. $44
D. $48
E. $56
Show more

Let's pick 10 units to make the math clean (works with both 4/5 and 9/10).

Step 1: Find the cost per unit using the original scenario.

The discounted price is 70% of $800 = $560.

Original scenario: 4/5 of 10 = 8 units sold at $800, and 2 units sold at $560.

Total revenue = (8 × $800) + (2 × $560) = $6,400 + $1,120 = $7,520

Average revenue per unit = $7,520 ÷ 10 = $752

Since average profit was $20, the cost per unit = $752 − $20 = $732.

Step 2: Calculate the new average profit.

New scenario: 9/10 of 10 = 9 units at $800, and 1 unit at $560.

Total revenue = (9 × $800) + (1 × $560) = $7,200 + $560 = $7,760

Average revenue per unit = $7,760 ÷ 10 = $776

New average profit = $776 − $732 = $44.

Answer: C

Key Insight: The cost per unit never changes — only the revenue mix changes. So the entire problem boils down to: (1) use the original scenario to back-solve for cost, then (2) plug the new sales mix in to find new average profit. Picking a smart number of units (like 10) keeps the fractions simple.
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