solve each problem by setting up and solving an appropriate system of equations. A small-town library buys a total of 35 books that cost $644.

remolatg

remolatg

Answered question

2021-09-08

solve each problem by setting up and solving an appropriate system of equations. A small-town library buys a total of 35 books that cost $644. Some of the books cost $16 each, and the remainder cost $20 each. How many books of each price did the library buy?

Answer & Explanation

Maciej Morrow

Maciej Morrow

Skilled2021-09-09Added 98 answers

A small-town library buys a total of 35 books that cost $644. Some of the books cost $16 each, and the remainder cost $20 each.

Let x & y be the number of books that costs $16 each and $20 each respectively.

Then, x+y=35(1) [Total books]

16x+20y=644(2) [Total cost]

Now, [16·Equation (1)]−[Equation (2)]

16(x+y)(16x+20y)=16(35)644

16x+16y16x20y=560644

4y=84

y=21

Now put y=21 in equation (1), we get

x+21=35

x=14

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