Question

Find all pairs of consecutive even positive integers, both of which are larger than5 such that their sum is less than 23.24.

Answer 1

Let x be the smaller even positive integer. Then, the larger consecutive even integer is x+2.

It is given that,

x>5(1)

x+2>5(2)

x+( x+2 )<23`(3)

Solve equation (3),

x+( x+2 )<23 2x+2<23 2x<21 x< 21 2 (4)

From equation (1) and (4),

5<x<10.5

Since x is an even number, therefore the values of x are different sets of even integers.

Thus, the pairs are ( 6,8 ),( 8,10 ),( 10,12 ).