# The sums of three whole numbers taken in pairs are 11, 12, and 17. What is the middle number (taken in orders)?

Jul 10, 2018

$3 , 8 , 9 \text{ are the 3 numbers}$

#### Explanation:

$\text{let the 3 numbers be a, b and c, then}$

$a + b = 11 \to \left(1\right)$

$b + c = 12 \to \left(2\right)$

$a + c = 17 \to \left(3\right)$

$\text{from equation } \left(1\right) \textcolor{w h i t e}{x} b = 11 - a$

$\text{from equation } \left(3\right) \textcolor{w h i t e}{x} c = 17 - a$

$\left(2\right) \to 11 - a + 17 - a = 12$

$- 2 a + 28 = 12 \Rightarrow - 2 a = - 16 \Rightarrow a = 8$

$\left(1\right) \to b = 11 - 8 = 3$

$\left(3\right) \to c = 17 - 8 = 9$

$\text{the 3 numbers are "3,color(red)(8)" and } 9$