Question 979391
A vending machine sells chips at $0.55 and candy at $0.75. Last month, the
vending machine yielded $189.00 with the sale of 280 items.
Let x be the number of chips sold and y the number of candies. How many packages
of chips were purchased last month?


<pre>
Let the number of chips be x
Let the number of candies be y
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
item        items      item      items
-------------------------------------------
chips         x      $0.55     $0.55x
candies       y      $0.75     $0.75y
-------------------------------------------
TOTALS      280      -----     $1890

 The first equation comes from the second column.

  {{{(matrix(3,1,Number,of,chips))}}}{{{""+""}}}{{{(matrix(3,1,Number,of,candies))}}}{{{""=""}}}{{{(matrix(4,1,total,number,of,items))}}}
  x + y = 280
  {{{(matrix(4,1,Value,of,ALL,chips))}}}{{{""+""}}}{{{(matrix(4,1,Value,of,ALL,candys))}}}{{{""=""}}}{{{(matrix(5,1,Total,value,of,ALL,items))}}}

0.55x + 0.75y = 1890

Get rid of decimals by multiplying every term by 100:

     55x + 75y = 18900

 So we have the system of equations:
{{{system(x + y = 280,55x + 75y = 18900)}}}.

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

  x + y = 280
      y = 280 - x

Substitute (280 - x) for y in 55x + 75y = 18900
 
     55x + 75(280 - x) = 18900
     55x + 21000 - 75x = 18900
          -20x + 21000 = 18900
                  -20x = -2100
                     x = 105 = the number of chips.

Substitute in y = 280 - x
              y = 280 - (105)
              y = 175 candies.
The number of candies is 280-x or 280-105 or 175 candies.

Checking:  105 chips is $0.55*105 = $57.75 and 
           175 candies is $0.75*175 = $131.25
            That's 280 items.
            And indeed $57.75 + $131.25 = $189.00
Edwin</pre>