Question 1034811
<pre>
Let the number of quarters be q
Let the number of dimes be d


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
quarters      q      $0.25       $0.25q
dimes         d      $0.10       $0.10d
-------------------------------------------
TOTALS       64      -----       $13.60

 The first equation comes from the number of coins column.

  {{{(matrix(3,1,Number,of,quarters))}}}{{{""+""}}}{{{(matrix(3,1,Number,of,dimes))}}}{{{""=""}}}{{{(matrix(4,1,total,number,of,coins))}}}
                 q + d = 64

 The second equation comes from the last column.
  {{{(matrix(4,1,Value,of,ALL,quarters))}}}{{{""+""}}}{{{(matrix(4,1,Value,of,ALL,dimes))}}}{{{""=""}}}{{{(matrix(5,1,Total,value,of,ALL,coins))}}}

           0.25q + 0.10d = 13.6

Get rid of decimals by multiplying every term by 100:

              25q + 10d = 1360

 So we have the system of equations:
           {{{system(q + d = 64,25q + 10d = 1360)}}}.

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

             q + d = 64
                 d = 64 - q

Substitute (64 - q) for d in 25q + 10d = 1360

    25q + 10(64 - q) = 1360
     25q + 640 - 10q = 1360
           15q + 640 = 1360
                 15q = 720
                   q = 48 = the number of quarters.

Substitute in d = 64 - q
              d = 64 - (48)
              d = 16 dimes.

Checking:  48 quarters is $12.00 and 16 dimes is $1.60
            That's 64 coins.
            And indeed $12.00 + $1.60 = $13.60
Edwin</pre>