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

1 Answer
Jun 27, 2015

Answer:

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#