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) About Me  (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) About Me  (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.