Question

Find two numbers whose difference is 8 but whose average is 13.

Answer 1

9 and 17

Explanation:

let x and y be the 2 numbers , x > y , then

x - y = 8 → (1)

`(x+y)/(2)` = 13 ( multiply both sides by 2 )

x + y = 26 → (2)

add both equations term by term to eliminate y

2x + 0 = 34

2x = 34 ( divide both sides by 2 )

x = 17

substitute x = 17 into (1) and solve for y

17 - y = 8 ( subtract 17 from both sides )

- y = - 9 ( multiply both sides by - 1 )

y = 9

The 2 numbers are 9 and 17

Answer 2

9 and 17

Explanation:

Let the two numbers by x and y.

We are told that x - y = 8

And we learn that (x+y)/2 = 13

Rearrange the first equation to isolate x (or y):

x - y = 8

x = 8+y

Use this expression for x in the second equation:

(x+y)/2 = 13

((8+y)+y)/2 = 13

Solve for y:

(2y+8)/2 = 13

y + 4 = 13

y = 9

If y = 9, x is:

x - y = 8

x - (9) = 8

x = 17

The difference between 17 and 9 is 8

The average is (9+17)/2 = 13