Evercool purchased several portable air conditioners. In J

Question

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

Dereno · Answer

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

kevincan · Answer

Five Kudos if anybody can provide a 20 second solution!

Dereno · Answer

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.

egmat · Answer

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.

himssss29 · Answer

C. $44 
 Setup:  Let cost per unit = C.

June scenario (4/5 at full price, 1/5 at 30% off): 
 
 Discounted price = 800 × 0.7 = $560 
 Average revenue per unit = (4/5)(800) + (1/5)(560) = 640 + 112 = $752 
 Average profit = $20, so: 752 − C = 20 →  C = 732   
 New scenario (9/10 at full price, 1/10 at 30% off): 
 
 Average revenue per unit = (9/10)(800) + (1/10)(560) = 720 + 56 = $776 
 Average profit = 776 − 732 =  $44

Evercool purchased several portable air conditioners. In J

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