SOLUTION: Hi, Bill sold 2 used books for $452 each. However the cost of each book was different. As a result a profit of 22% was made on the first book sold but a loss of 22% was made on th

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Question 195553: Hi,
Bill sold 2 used books for $452 each. However the cost of each book was different. As a result a profit of 22% was made on the first book sold but a loss of 22% was made on the second sale. What is Bill's total profit or loss on both books.
Can you please explain how to do this problem?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let f="cost of 1st book" and s="cost of 2nd book"

the profit (or loss) on an item is the difference between the cost and the selling price

the percentage profit/loss is the amount of profit/loss divided by the cost

.22 = (452-f) / f
multiplying by f ___ .22f = 452-f
adding f ___ 1.22f = 452
dividing by 1.22 ___ f = 370.49
profit = 452 - 370.49 = 81.51

-.22 = (452-s) / s
multiplying by s ___ -.22s = 452-s
adding s ___ .78s = 452
dividing by .78 ___ s = 579.49
loss = 452 - 579.49 = -127.49

so, the total LOSS on both books is 81.51 - 127.49 or -45.98