Question

THE SUM OF THREE CONSECUTIVE EVEN INTEGERS IS 72 FIND THE THIRD INTEGERS.​

Answer 1

Answer: The three consecutive even numbers are 22, 24, 26

22+24+26 = 72

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Explanation:

• x = first even number
• x+2 = second even number directly right after x
• (x+2)+2 = x+4 = third even number directly after x+2

For example, if x = 12, then we'd have x+2 = 12+2 = 14 and x+4 = 14+4 = 18.

However 12+14+18 = 44 is not 72 like we want.

You can guess-and-check your way to the answer, but a faster efficient route is to use algebra. Add up those x expressions and set the sum equal to 72 and solve.

(first) + (second) + (third) = 72

(x) + (x+2) + (x+4) = 72

3x+6 = 72

3x = 72-6

3x = 66

x = 66/3

x = 22

So we have,

• x = 22 = first even number
• x+2 = 22+2 = 24 = second even number
• x+4 = 22+4 = 26 = third even number

As a check: 22+24+26 = 72 which verifies the answers.