Question

My teacher didn't go over this and we have to show work

Find three consecutive even integers such that the sum of twice the smallest number and three times the largest is 42.

Answer 1

The three consecutive even integers are 6, 8, 10

Explanation:

• The difference between each two consecutive even numbers is 2

• Assume that the first number is x, then the other two numbers are x + 2 and x + 4

∵ The three consecutive even numbers are x, x + 2, x + 4

∵ The smallest number is x

∴ Twice the smallest number = 2x ⇒ (1)

∵ The largest number is x + 4

∴ Three times the largest number = 3(x + 4) = 3(x) + 3(4)

∴ Three times the largest number = 3x + 12 ⇒ (2)

∵ The sum of twice the smallest number and three times the largest is 42

→ Add (1), (2) and equate the sum by 42

∴ 2x + 3x + 12 = 42

→ Add the like terms

∴ 5x + 12 = 42

→ Subtract 12 from both sides

∴ 5x + 12 - 12 = 42 - 12

∴ 5x = 30

→ Divide both sides by 5

∵
`(5x)/(5)=(30)/(5)`

∴ x = 6

∴ The smallest integer is 6

∴ The middle integer is 6 + 2 = 8

∴ The largest integer is 6 + 4 = 10

∴ The three consecutive even integers are 6, 8, 10