Question

If the product of two consecutive even integers is 76 less than 10 times their sum, how do you find the two integers?

Answer 1

There are two possible solutions - `4` and `6` or `14` and `16`

Explanation:

First put the statement into mathematical terms. Let `x` be the first integer, then the second one is `x+2`.

Then the product `x(x+2)=10(x+(x+2)) -76`

Expanding,
`x^2+2x=20x+20-76`
`x^2-18x+56=0`
`(x-14)(x-4)=0`

Then `x=14` or `x=4` and the second integer is `16` or `6`