Question 1035410
Kevin and Randy Muise have a jar containing 
28 coins, all of which are either quarters or nickels. 
The total value of the coins in the jar is $4.00. 
How many of each type of coin do they have?
<pre>
Let the number of quarters be x
Let the number of nickels be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
quarters      x      $0.25       $0.25x
nickels       y      $0.05       $0.05y
-------------------------------------------
TOTALS       28      -----       $4.00

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

  {{{(matrix(3,1,Number,of,quarters))}}}{{{""+""}}}{{{(matrix(3,1,Number,of,nickels))}}}{{{""=""}}}{{{(matrix(4,1,total,number,of,coins))}}}
                 x + y = 28

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

  {{{(matrix(4,1,Value,of,ALL,quarters))}}}{{{""+""}}}{{{(matrix(4,1,Value,of,ALL,nickels))}}}{{{""=""}}}{{{(matrix(5,1,Total,value,of,ALL,coins))}}}

           0.25x + 0.05y = 4

Get rid of decimals by multiplying every term by 100:

                25x + 5y = 400

 So we have the system of equations:
           {{{system(x + y = 28,25x + 5y = 400)}}}.

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

           x + y = 28
               y = 28 - x

Substitute (28 - x) for y in 25x + 5y = 400

    25x + 5(28 - x) = 400
     25x + 140 - 5x = 400
          20x + 140 = 400
                20x = 260
                  x = 13 = the number of quarters.

Substitute in y = 28 - x
              y = 28 - (13)
              y = 15 nickels.

Checking:  13 quarters is $3.25 and 15 nickels is $0.75
            That's 28 coins.
            And indeed $3.25 + $0.75 = $4.00
Edwin</pre>