SOLUTION: 3 apples and a pineapple equally balances 10 oranges.also,6 oranges and an apple equally balance a pineapple.how many oranges balance a pineapple?

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Question 1010157: 3 apples and a pineapple equally balances 10 oranges.also,6 oranges and an apple equally balance a pineapple.how many oranges balance a pineapple?
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
a, the unit for one apple
p, the unit for one pineapple
n, the unit for one OraNge
system%283a%2Bp=10n%2C6n%2Ba=p%29

system%283a=10n-p%2Ca=p-6n%29

a=%2810n-p%29%2F3=p-6n

10n-p=3%28p-6n%29

10n-p=3p-18n

10n%2B18n-p=3p

18n=4p

p=18n%2F4

p=%289%2F2%29n

highlight%28p=%284%261%2F2%29n%29

One pineapple will balance four and a half oranges.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor's answer is wrong.


Let the number of ounces an Apple weighs be A
Let the number of ounces a Pineapple weighs be P
Let the number of ounces an Orange weighs be Q 

[Can't use O for the number of ounces an Orange
weighs because O looks too much like zero 0, and Q 
looks the most like O without looking too much like 
zero. :)  ]

>>3 apples and a pineapple equally balances 10 oranges.<<
3A + P = 10Q

>>also,6 oranges and an apple equally balance a pineapple.<<
6Q + A = P

>>how many oranges balance a pineapple?<<
Let the answer be N

Then NQ = P

So we have the system  

1)   3A + P = 10Q   
2)   6Q + A = P
3)   NQ = P

Solve 2) for A

4)   A = P - 6Q

Substitute in 1)

5)   3(P - 6Q) + P = 10Q
      3P - 18Q + P = 10Q
          4P - 18Q = 10Q
                4P = 28Q
6)               P = 7Q
Substitute 6) into 3)

     NQ = 7Q
      N = 7

Answer: It takes 7 oranges.

There's not enough information given to find out how
many ounces any of the fruit weighs, but regardless
it would always take 7 oranges to balance a pineapple.
All we can tell is that substituting 6) into 4) we get
that oranges and apples weigh the same and a pineapple 
weighs 7 times as much as they weigh each. 

Edwin