Question 924248
Mackenzie has 19 coins in her pocket. They are all either dimes or quarters, totaling $3.40.
<pre>
Let the number of dimes be D
Let the number of dimes be Q   
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
DIMES        D        $0.10    $0.10D 
QUARTERS     Q        $0.25    $0.25Q
-------------------------------------------
TOTALS      19        -----    $3.40

 The equations comes from the "Number of coins" column 
and the "Value of ALL coins" column:

{{{(matrix(3,1,Number,of,dimes))}}}{{{""+""}}}{{{(matrix(3,1,Number,of,quarters))}}} {{{""=""}}} {{{(matrix(3,1,Number,of,coins))}}}


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

{{{system(D+Q=19,

0.10D + 0.25Q = 3.40)}}}

Get rid of decimals in the second by multiplying 
every term by 100

    10D + 25Q = 340

{{{system(D+Q=19,

10D + 25Q = 340)}}}

Solve the first for D

D+Q=19
  D=19-Q

Substitute in

     10D + 25Q = 340
10(19-Q) + 25Q = 340
 190-10Q + 25Q = 340
       190+15Q = 340
           15Q = 150 
             Q = 10 quarters

             D = 19-Q = 19-10 = 9 dimes

Edwin</pre>