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?

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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) About Me  (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 x%2By=54. Also, since "some cost $32 each and some cost $44 each. the total cost of the books was $1968", this tells us that 32x%2B44y=1968





So we have the system of equations:

system%28x%2By=54%2C32x%2B44y=1968%29


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

x%2By=54 Start with the first equation


y=54-x Subtract x from both sides


y=-x%2B54 Rearrange the equation

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

Since y=-x%2B54, we can now replace each y in the second equation with -x%2B54 to solve for x



32x%2B44highlight%28%28-x%2B54%29%29=1968 Plug in y=-x%2B54 into the second equation. In other words, replace each y with -x%2B54. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



32x%2B%2844%29%28-x%29%2B%2844%29%2854%29=1968 Distribute 44 to -x%2B54


32x-44x%2B2376=1968 Multiply


-12x%2B2376=1968 Combine like terms on the left side


-12x=1968-2376Subtract 2376 from both sides


-12x=-408 Combine like terms on the right side


x=%28-408%29%2F%28-12%29 Divide both sides by -12 to isolate x



x=34 Divide





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


So the first part of our answer is: x=34









Since we know that x=34 we can plug it into the equation y=-x%2B54 (remember we previously solved for y in the first equation).



y=-x%2B54 Start with the equation where y was previously isolated.


y=-%2834%29%2B54 Plug in x=34


y=-34%2B54 Multiply


y=20 Combine like terms



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


So the second part of our answer is: y=20









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

So our answers are:


x=34 and y=20


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