SOLUTION: 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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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       Log On


   

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?
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
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? 

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.

  %28matrix%283%2C1%2CNumber%2Cof%2Cchips%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2Ccandies%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Citems%29%29
  x + y = 280
  %28matrix%284%2C1%2CValue%2Cof%2CALL%2Cchips%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2Ccandys%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Citems%29%29

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%28x+%2B+y+=+280%2C55x+%2B+75y+=+18900%29.

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