Justin is exchanging dollars for rolls of quarters and rolls of dimes at a bank. Each roll of quarters has a value of $10 and each roll of dimes has a value of

Question

 Justin is exchanging dollars for rolls of quarters and rolls of dimes at a bank. Each roll of quarters has a value of $10 and each roll of dimes has a value of $5. He exchanges $90 and receives 11 rolls of coins. How many of each type of roll of coins did he receive?

Answer 1

There are two important equations:

  (1) how much total money

  (2) how many rolls of coins

 

Set x = number of rolls of quarters

      y = number of rolls of dimes

 

The value of each type of coin is:  (value per roll)*(number of rolls).

            Total value             =      value of quarters      +       value of dimes

"He exchanges $90 "   means

[eq1]       $90                    =          $10x                    +           $5y

 

[eq2]   "11 rolls of coins"    means     x + y = 11

 

Let's substitute for y:

      y = 11 - x                 [solve for y in eq2]

     90 = 10x + 5(11-x)        [put that value into eq1]

     90 = 10x + 55 - 5x

     35 = 5x

       7 = x

 There are 7 rolls of quarters.

 

Now, substitute that value for x in either equation (which is easier?):

   7 + y = 11

       y = 4

  There are 4 rolls of dimes.

 

Checking (very important):

  Is    90 = 10(7) + 5(4)   ?     [eq1]

         90 = 70 + 45   ?

         90 = 90   ?yes

  Is    7 + 4 = 11   ?    [eq2]

           11 = 11   ? yes