SOLUTION: Jane had 12 coins in her purse that have a total of $1. If these coins consist of nickels and dimes, how many of each does she have?

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Question 1020549: Jane had 12 coins in her purse that have a total of $1. If these coins consist of nickels and dimes, how many of each does she have?
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Let the number of nickels be x
Let the number of dimes be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels       x      $0.05       $0.05x
dimes         y      $0.10       $0.10y
-------------------------------------------
TOTALS       12      -----       $1.00

 The first equation comes from the second column.

  
                 x + y = 12

 The second equation comes from the last column.
  

           0.05x + 0.10y = 1

Get rid of decimals by multiplying every term by 100:

                5x + 10y = 100

 So we have the system of equations:
           .

We solve by substitution.  Solve the first equation for y:

                   x + y = 12
                       y = 12 - x

Substitute (12 - x) for y in 5x + 10y = 100

         5x + 10(12 - x) = 100
          5x + 120 - 10x = 100
               -5x + 120 = 100
                     -5x = -20
                       x = 4 = the number of nickels.

Substitute in y = 12 - x
              y = 12 - (4)
              y = 8 dimes.


Checking:  4 nickels is $0.20 and 8 dimes is $0.80
            That's 12 coins.
            And indeed $0.20 + $0.80 = $1.00
Edwin
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