Trader Percentages
Algebra
Level
3
Trader Tate sold 2 trucks for $10000 each.
On the first truck, he made a 10% profit.
On the second truck, he made a 10% loss.
In total, did Trader Tate make a profit, make a loss, or break even?
Profit
Break even
Loss
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1 solution
On the first truck, since he made a profit of 10%, the selling price is 110% of the purchase price. Thus, the purchase price is 1 1 0 1 0 0 × 1 0 0 0 0 = 9 0 9 0 . 9 0 .
On the second truck, since he made a loss of 10%, the selling price is 90% of the purchase price. Thus, the purchase price is 9 0 1 0 0 × 1 0 0 0 0 = 1 1 1 1 1 . 1 1 .
Hence, the combined purchase price is 1 1 1 1 1 . 1 1 + 9 0 9 0 . 9 0 = 2 0 2 0 2 . 0 2 . So Trader Tate made a loss.
We can show that if the trucks sold for the same price, and the percentage profit and loss are the same x % , then the trader will have made a loss. This is because the purchase price would be
1 0 0 + x 1 0 0 + 1 0 0 − x 1 0 0 = 1 0 0 0 0 − x 2 2 0 0 0 0 > 2