The lesser of two consecutive even integers is 10 more than one-half the greater. Find the integers.

Hello,

Here's my solution:

Let n = the lesser of the two consecutive even integers; so what will be a good way to represent the greater of the two consecutive even integers? I say n + 2.

Let's write the equation:

n = ((n+2) / 2) + 10

I'll multiply both sides of the equation by 2 to eliminate the denominator, getting:

2n = 2[ ((n+2) / 2) + 10]

This reduces to:

2n = n+2 + 20

Which can be further simplified to:

2n = n+22

Subtracting n from both sides we get:

n = 22

So n, the lesser consecutive even integer is 22. The greater consecutive even integer is 24.

Let's check this solution by substituting n = 22 into our original equation:

n = ((n+2) / 2) + 10

22 = ((22+2) / 2) + 10

22 = ((24) / 2) + 10

22 = (12) + 10

22 = 22 - it checks!