Question

12. Find three consecutive even integers such that

the sum of the smallest integer and twice the
median integer is 20 more than the largest
integer.

Answer 1

10, 11, 12

Explanation:

Hi there!

Let x be equal to the smallest integer.

Let x+1 and x+2 be equal to the consecutive integers.

We're given that:

⇒ smallest integer + 2 × middle integer = 20 + largest integer

Construct an equation:

`(x)+2(x+1)=20+(x+2)`

Combine like terms:

`(x)+2(x+1)=20+(x+2)\\x+2x+2=20+x+2\\3x+2=22+x\\2x=20\\x=10`

Therefore, the smallest integer is 10.

This makes the consecutive integers 11 and 12.

I hope this helps!