SOLUTION: jake has 2.50 worth of nickels and dimes.she has 36 coins in total. how many nickels and dimes does she have

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       36      -----       $2.50

 The first equation comes from the "Number of coins" column.

  

                   x + y = 36

 The second equation comes from the "Value of all coins" column.
  

           0.05x + 0.10y = 2.5

Get rid of decimals by multiplying every term by 100:

                5x + 10y = 250

 So we have the system of equations:
           .

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

                   x + y = 36
                       y = 36 - x

Substitute (36 - x) for y in 5x + 10y = 250

         5x + 10(36 - x) = 250
          5x + 360 - 10x = 250
               -5x + 360 = 250
                     -5x = -110
                       x = 22 = the number of nickels.

Substitute in y = 36 - x
              y = 36 - (22)
              y = 14 dimes.

Checking:  22 nickels is $1.10 and 14 dimes is $1.40
            That's 36 coins.
            And indeed $1.10 + $1.40 = $2.50
Edwin