Question

find two consecutive even integers such that the smaller added to three times the larger is equal to 150

Answer 1

• Even Integer Pattern: n, n + 2, n + 4, n + 6, etc.
• Let x = smaller integer

So firstly, our two integers are x and x + 2. And we know that the sum of the smaller integer, x, and 3 times the larger integer, x + 2, is 150. Using what we know, our equation is
`x+3(x+2)=150`

Firstly, foil 3(x + 2):
`x+3x+6=150`

Next, combine like terms:
`4x+6=150`

Next, subtract 6 on both sides:
`4x=144`

And lastly, divide 4 on both sides and your answer will be
`x=36`

Now since we know that the smaller integer is 36, add 2 to 36 to get the larger integer, which is 38.

In short, the smaller integer is 36 and the larger integer is 38.