Question

If the sum of five consecutive even integers is 90, what is the smallest of the five integers?

Answer 1

So the pattern of even integers is: 2, 4, 6, 8, etc. They are always 2 more than the prior even integer. Using this knowledge, our 5 consecutive even numbers are (let x = smallest even number): x, x + 2, x + 4, x + 6, and x + 8.

Now that we have the numbers, we can form our equation as such: $x+x+2+x+4+x+6+x+8=90$ . From here we can solve for x.

Firstly, combine like terms: $5x+20=90$

Next, subtract 20 onto both sides of the equation: $5x=70$

Lastly, divide both sides by 5 and your smallest integer is $x=14$