lheiannie07 wrote:Tom and Aly purchased a laptop each at the same price. Both of them marked up the price of their laptops by the same amount. Aly sold her laptop by offering successive discounts of $200 and 20%, in that order; whereas Tom sold his laptop by offering the same scheme of discount but in reverse order. If the profit made by Aly was equal to the loss incurred by Tom, then what was the amount of profit (in $) made by Aly?
(A) $20
(B) $25
(C) $30
(D) $35
(E) $40
We can let p = the price of the laptops when Tom and Aly bought them and m = markup of the laptops. Thus, p + m = the price at which they originally wanted to sell the laptops. However, after the discounts, Aly sold her laptop at the price of (p + m - 200)(0.8) dollars and Tom sold his laptop at the price of 0.8(p + m) - 200 dollars. In dollars, the profit made by Aly is (p + m - 200)(0.8) - p and the loss incurred by Tom is p - (0.8(p + m) - 200). Since Aly's profit is equal to Tom's loss, we can create the following equation:
(p + m - 200)(0.8) - p = p - (0.8(p + m) - 200)
0.8p + 0.8m - 160 - p = p - 0.8p - 0.8m + 200
0.8m - 0.2p - 160 = 0.2p - 0.8m + 200
1.6m - 0.4p = 360
16m - 4p = 3600
4p = 16m - 3600
p = 4m - 900
At this point, we actually can make up a number for m (as long as p will be positive). For example, we can let m = 250, so p = 4(250) - 900 = 100. Thus, Aly's profit is:
(100 + 250 - 200)(0.8) - 100
(150)(0.8) - 100
120 - 100
20 dollars
Note: For any number we make up for m (as long as p will be positive), Aly's profit will always be $20.
Alternatively, we can substitute p = 4m - 900 in the equation for the profit of Aly:
Profit of Aly = (p + m - 200)(0.8) - p
= (4m - 900 + m -200)(0.8) - (4m - 900)
= (5m - 1100)(0.8) - 4m + 900
= 4m - 880 - 4m + 900
= 20
Answer:
A
