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. :)  ]   

3A + P = 10Q

6Q + A = P

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