A school will receive 40 volleyballs or basketballs. The basketballs are $25 and volleyballs are $15. If you spend $750 how many of each will you get?

Question

I need to see how to set up and solve

Answer 1

There is only one way to get 40 items for $750 (because they are priced differently),

 

The important key to realize is:  the total cost for volleyballs is $15*(number of volleyballs)

    , , , similarly for basketballs

 

Let x = number of volleyballs

      y = number of basketballs

Translate:

  '40 volleyballs or basketballs'       means       x+y = 40     [eq1]

 

"basketballs are $25 and volleyballs are $15. If you spend $750"

     cost for basketballs     +       cost for volleyballs      =      $750

           $25y                    +                 $15x              =     $750    [eq2]

               [note: be sure to put correct values together]

 

Solve for either x or y in eq1, then substitute that into eq2.

      x = 40 - y

 

     $25y +   $15x = $750

     $25y +   $15(40-y) = $750

      $25y + $600 - $15y = $750

           10y = 150

             y = 15

 

    x + 15 = 40

        x = 25

 

There are 15 volleyballs and 25 basketballs.

 

Check:

  Is     $25(15) + $15(25) = $750   ?

            $375    +  $375   = $750   ?

                  $750   =   $750   ?yes