Question

When three numbers are added two at a time, the sums are 29, 46, 53. What is the sum of all three numbers?

Answer 1

`Sum = 64`

Explanation:

Let the three numbers be a, b and c; such that:

`a + b = 29` ---- (1)

`b + c = 46` --- (2)

`a + c = 53` --- (3)

Subtract equation 2 from 3

`a - b + c - c = 53 - 46`

`a - b = 7` --- (4)

Add this equation to the (1)

`a + a + b - b = 29 + 7`

`2a= 36`

Solve for a

`a = 36/2`

`a = 18`

Substitute 18 for a in (1)

`a + b = 29`

`18 + b = 29`

Solve for b

`b = 29 - 18`

`b = 11`

Substitute 11 for b in (2)

`b + c = 46`

`11 + c = 46`

Solve for c

`c = 46 - 11`

`c = 35`

`Sum = a + b +c`

`Sum = 18 + 11 + 35`

`Sum = 64`