There are a total of 50 apples and pears (apples + pears) in a large basket. If the total number of apples was doubled and the total number of pears was tripled, these two numbers would add up to 130. How many apples and pears are in the basket?

Solve this simultaneously.

Where a= apples and p= pears,

a+p=50 and 2a+3p=130

Multiply a+p=50 by 2 on both sides to get:

2a+2p=100

Then subtract the two equations from each other:

2a+3p=130

2a+2p=100

---------------     -->  2a-2a=0 ; 3p-2p=p ; 130-100=30

0+p=30

So p=30 (number of pears)

Which means that a is:

a+p=50 , where p=30

a+30=50

a=50-30=20 (number of apples)