SOLUTION: If I just sold my two books at $990 each. On one I gained 10% and on the other one I lost 10%. Then. (a) I lost $20. (b) I gained $918. (c) I gained $19.8. (d) None of these.

Question 1081202: If I just sold my two books at $990 each. On one I gained 10% and on the other one I lost 10%. Then.
(a) I lost $20.
(b) I gained $918.
(c) I gained $19.8.
(d) None of these.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let
x = original value of book1
y = original value of book2
this is at the point in time when you are buying each book (not selling)

you bought book1 for x dollars and turn around to sell it for 990 dollars. The difference in price is 990-x which is some positive number (since you gain money for selling this book).

Divide this difference over the original price x to get (990-x)/x. This ratio will result in the decimal value 0.10 which represents a 10% gain. So we have this equation (990-x)/x = 0.10

Let's solve for x
(990-x)/x = 0.10
x*(990-x)/x = x*0.10
990-x = 0.10x
990-x+x = 0.10x+x
990 = 1.10x
1.10x = 990
1.10x/(1.10) = 990/(1.10)
x = 900

So the original value of book1 is $900. This is the value in which you buy it at.

In other words, you bought book1 for $900 and sold it $990.

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Similarly, the second equation would be
(990-y)/y = -0.10
Notice how the right hand side is negative to indicate a loss. The left side is identical to the first equation (use y instead of x).

Solve for y
(990-y)/y = -0.10
y*(990-y)/y = y*(-0.10)
990-y = -0.10y
990-y+y = -0.10y+y
990 = 0.90y
0.90y = 990
0.90y/(0.90) = 990/(0.90)
y = 1100

So you bought book2 for $1100 and then later sold it for $990.

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Recapping so far:

you buy book1 for $900 and sell it later for $990.

you buy book2 for $1100 and sell it later for $990.

In the case of book1, you have a profit of
(new value) - (old value) = 990-900 = 90 dollars

In the case of book2, you have a profit of
(new value) - (old value) = 990-1100 = -110 dollars
Note: the negative profit means a loss

The two profits (90 and -110) are then combined to get this overall net profit: 90 + (-110) = -20
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At the end of the day, the net profit comes out to -20 dollars indicating that you lost $20.

Answer: Choice (a) I lost $20
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