Question

The sums of 3 whole numbers taken in pairs are 12, 17 and 19. What is the least number?

Answer 1

The least is 5

Explanation:

Represent the numbers with x, y and z.

Such that:

`x + y = 12`

`y + z = 17`

`x + z = 19`

Required

Determine the smallest number

Add the three equations:

`(x + y) + (y + z) + (x + z) = 12 + 17 + 19`

`(x + y) + (y + z) + (x + z) = 48`

Collect Like Terms

`x + x + y + y + z + z = 48`

`2x + 2y + 2z= 48`

Divide through by 2

`x + y +z = 24`

Recall that:

`x + y = 12`

`y + z = 17`

`x + z = 19`

Substitute 12 for x + y in
`x + y +z = 24`

`12 + z =24`

`z = 24-12`

`z = 12`

Substitute 17 for y + z in
`x + y +z = 24`

`x + 17 = 24`

`x = 24-17`

`x = 7`

Substitute 19 for x + z in
`x + y +z = 24`

`19 + y = 24`

`y = 24 - 19`

`y = 5`

So:

The numbers are 7, 5 and 12 and the least is 5