A and B have some apples. If A gives 2 apples to B, then A will have half of…

Step-by-Step Solution
To solve this problem, we can set up a system of equations based on the two scenarios provided:

Define Variables:

Let A be the number of apples person A has.

Let B be the number of apples person B has.

Translate Conditions into Equations:

Condition 1: "If A gives 2 apples to B, then A will have half of the apples that B has."

A - 2 = (B + 2) / 2

Multiply both sides by 2: 2A - 4 = B + 2

Equation 1: 2A - B = 6

Condition 2: "If B gives 10 apples to A, then their number of apples will be the same."

A + 10 = B - 10

Equation 2: B - A = 20

Solve the System of Equations:

Add Equation 1 and Equation 2 together:
(2A - B) + (B - A) = 6 + 20
A = 26

Substitute A = 26 into Equation 2:
B - 26 = 20
B = 46

Person A has 26 apples, and person B has 46 apples.

Final Calculation:

The question asks for the total number of apples both A and B have combined: 26 + 46 = 72.