Find the largest of three consecutive even integers when six times the first integers is equal to fi

[math_celebrity]

Find the largest of three consecutive even integers when six times the first integers is equal to five times the middle integer.

Let the first of the 3 consecutive even integers be n.
The second consecutive even integer is n + 2.
The third (largest) consecutive even integer is n + 4.

We are given 6n = 5(n + 2).

Multiply through on the right side, and we get:
6n = 5n + 10

Typing 6n = 5n + 10 into the search engine, we get n = 10.

Remember, n was our smallest of 3 consecutive even integers. So the largest is:
n + 4
10 + 4
14