Question

Half of the difference of two numbers is 2. The sum of the greater number and twice the smaller number is 13. Find the numbers.

Answer 1

Given: Let the greater number = x and the smaller number = y.

Half of their difference is 2: `(x - y)/2 = 2`.

The sum of the greater and twice the smaller is 13: x + 2y = 13.

Step-wise calculation:

1. From `(x - y)/2 = 2`, multiply both sides by 2:

x – y = 4

2. Now solve the system:

x – y = 4

x + 2y = 13

3. Subtract the first equation from the second:

(x + 2y) – (x – y) = 13 – 4

⇒ 3y = 9

⇒ y = 3

4. Substitute y = 3 into x – y = 4

⇒ x – 3 = 4

⇒ x = 7

The numbers are 7 (greater) and 3 (smaller).