Question

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

Answer 1

Pairs of consecutive even integers whose sum is greater than 72 but less than 79 are:
`color(white)("XXXX")` `(36,38) and (38,40)`

Explanation:

Let `x` be the smaller of the two consecutive even integers
`rarr` the larger is `x+2`

Part 1: The sum is greater than 73
`color(white)("XXXX")` `rarr (x) + (x+2) > 73`
`color(white)("XXXX")` `rarr 2x > 71`
`color(white)("XXXX")` `rarr x > 35.1`
and since x is an even integer, `x>=36`

Part 2: The sum is less than 79
`color(white)("XXXX")` `rarr (x)+(x+2)<79`
`color(white)("XXXX")` `rarr 2x<77`
`color(white)("XXXX")` `rarr x < 38.5`
and since `x` is an even integer `x <=38`