Question

Aaron and Henry had 52 grapes. If Aaron ate 11 grapes and gave 5 grapes to Henry, he would have 19 fewer grapes than Henry. How many grapes did Henry have in the beginning?

Answer 1

Let A be the number of Aaron's grapes and H be the number of Henry grapes. Then we've got the next system of equations:

A + H = 52
A - 11 - 5 = H + 5 - 19

Let's solve it.
&
A + H = 52
A - 16 = H - 14

A + H = 52& (1)
A = H + 2& (2)

Let's substitute (2) into (1):

H + 2 + H = 52 ==> 2H = 50 ==> H = 25.

Then

A = H + 2 = 25 + 2 = 27.

So, Aaron had 27 grapes and Henry had 25 ones.