P6 Math: Apples and Oranges in Two Boxes

There are 200 apples and 90 oranges in Basket X.

There are 80 apples and 100 oranges in Basket Y.

Find the total number of apples and oranges that must be transferred from Basket X to Basket Y so that 4/5 of the fruits in Basket X and 1/2 of the fruits in Basket Y are apples.

Solution:

It is another mixed of ratio and algebra process that need to be mastered.

To start with, the solution involves number of apples and oranges, which the total is NOT CHANGED before and after the transfer.

Total num of apples = 200 + 80 = 280.

Total num of oranges = 80 + 100 = 180.

At the end of transfer, the ratio of fruits in each box will be:

Be careful the ratio in each box has different unit, so we should interpret it like:

Now it is safe to put in algebraic equation such as

(Apples)    4u + 1p = 280

(Oranges) 1u + 1p = 180

Solves the equation, to get 1p = 160 and 1u = 30.

At the end in box Y, there should be 160 apples and 160 oranges. It means we need to transfer (160 - 80) = 80 apples and (160 - 100) = 60 oranges from box X.