SOLUTION: in a stack of books 81 cm high, we have a total of 21 books. there are 5 cm thick and others of 3 cm thick. how do we each thickness?

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Question 138996: in a stack of books 81 cm high, we have a total of 21 books. there are 5 cm thick and others of 3 cm thick. how do we each thickness?
Answer by solver91311(24713) About Me  (Show Source):
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Number of thick books: x
Number of thin books: y

Total number of books: 21, so:

x%2By=21

The total thickness of all of the thick books is 5x, because each of the x thick books accounts for 5 cm.

The total thickness of all of the thin books is 3y.

Together, the books make a stack that is 81 cm tall, so:

5x%2B3y=81

Multiply the first equation by -3:
-3x-3y=-63

Now notice that the coefficients on the y terms in the two equations are additive inverses, that is to say: -3%2B3=0.

Just add the two equations term by term:
-3x-3y=-63
5x%2B3y=81

5x-3x%2B3y-3y=81-63
2x=18

And divide by 2:
x=9

So there are 9 thick (5cm) books and 21 - 9 = 12 thin (3 cm) books.

Check your answer:
9 * 5 = 45
12 * 3 = 36
45 + 36 = 81: Answer checks.