Question

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

Answer 1

Answer:

The least is 5

Step-by-step 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