SOLUTION: a local library bought 54 books. some cost $32 each and some cost $44 each. the total cost of the books was $1968. How many of the 32 dollar books were purchased?

Question 162958: a local library bought 54 books. some cost $32 each and some cost $44 each. the total cost of the books was $1968. How many of the 32 dollar books were purchased?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=# of $32 books and y=# of $44 books

Since "a local library bought 54 books", this means that . Also, since "some cost $32 each and some cost $44 each. the total cost of the books was $1968", this tells us that

So we have the system of equations:

Let's solve the system by use of substitution

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

---------------------

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Combine like terms on the left side

Subtract 2376 from both sides

Combine like terms on the right side

Divide both sides by -12 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

This means that 34 $32 books and 20 $44 books were purchased
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