SOLUTION: Four oranges, three apples and two papayas cost $15.50. Two oranges and six papayas cost $28.60. Three oranges and four apples cost $6.80. How much does each type of fruit cost?

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Question 1141355: Four oranges, three apples and two papayas cost $15.50. Two oranges and six papayas cost $28.60. Three oranges and four apples cost $6.80. How much does each type of fruit cost?
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
x = price of 1 apple
y = price of 1 papaya
z = price of 1 orange

Four oranges, three apples and two papayas cost $15.50. 

4x + 3y + 2z = $15.50

Two oranges and six papayas cost $28.60. 

2z + 6y = $28.60

Three oranges and four apples cost $6.80. 

3z + 4x = $6.80

Line up the three equations so that all variables are in
a vertical column:

(1)     4x + 3y + 2z = $15.50
(2)          6y + 2z = $28.60
(3)     4x      + 3z = $ 6.80

Subtract (3) from (1), call it (4)

(1)     4x + 3y + 2z = $15.50
(3)     4x      + 3z = $ 6.80
-----------------------------
(4)          3y -  z = $ 8.70

Line up (2) and (4)


(2)          6y + 2z = $28.60
(4)          3y -  z = $ 8.70

Multiply (4) by 2, call it (5), then add them

(2)          6y + 2z = $28.60
(5)          6y - 2z = $17.40
-----------------------------
            12y      = $46.00
              y      = $ 3.83 1/3 <-- price of 1 papaya

Substitute in (4)

(4) 3(3.83 1/3) -  z = $ 8.70
         $11.50 -  z = $ 8.70
                  -z = -$2.80
                   z =  $2.80  <-- price of 1 orange.

Substitute in (3)

(3)    4x + 3($2.80) = $ 6.80
          4x + $8.40 = $ 6.80
                  4x = -$1.60
                   x = -$0.40  <-- since it's negative, the apples are so
                                   rotten, that the store will pay you 40
                                   cents to take them to get rid of them.
                                  
 Edwin
Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!


Edwin -- you mixed up your variables in writing the equations....

The problem has a reasonable solution.
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