# How do you find all pairs of consecutive even integers whose sum is greater than 73 but less than 79?

Jun 27, 2015

Pairs of consecutive even integers whose sum is greater than 72 but less than 79 are:
$\textcolor{w h i t e}{\text{XXXX}}$$\left(36 , 38\right) \mathmr{and} \left(38 , 40\right)$

#### Explanation:

Let $x$ be the smaller of the two consecutive even integers
$\rightarrow$ the larger is $x + 2$

Part 1: The sum is greater than 73
$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow \left(x\right) + \left(x + 2\right) > 73$
$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow 2 x > 71$
$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow x > 35.1$
and since x is an even integer, $x \ge 36$

Part 2: The sum is less than 79
$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow \left(x\right) + \left(x + 2\right) < 79$
$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow 2 x < 77$
$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow x < 38.5$
and since $x$ is an even integer $x \le 38$