We are required to find three consecutive even integers such that the sum of twice the smallest number and three times the largest is 42.
let
the smallest even integer = x
the smallest even integer = xMiddle even integer = x + 2
the smallest even integer = xMiddle even integer = x + 2Largest even integer = x + 4
Sum of twice the smallest number and three times the largest is 42
2(x) + 3(x + 4) = 42
open parenthesis
2x + 3x + 12 = 42
collect like terms
5x = 42 - 12
5x = 30
divide both sides by 5
x = 30 / 5
x = 6
Therefore, the three consecutive numbers are:
the smallest even integer = x
= 6
Middle even integer = x + 2
= 6 + 2
= 8
Largest even integer = x + 4
= 6 + 4
= 10
The numbers are 6, 8, 10
Read more:
https://brainly.com/question/18867131
