The product of two consecutive even integers is 46 less than 9 times their sum.

Answer 1

We can set up a single equation to solve this, but we will use only one variable to represent both integers. Since they are consecutive even integers, let's let x = the first even integer and let x + 2 be the 2nd consecutive even integer.

By the wording of the problem, the equation will be as follows: x( x+2 ) = 9( x + (x+2)) - 46. Eliminating parentheses, we have x² + 2x = 18x + 18 - 46. Moving everything to one side and setting the equation equal to 0, the equation becomes x² - 16x + 28 = 0.

Since this is factorable, we will factor the trinomial and use the Zero Product Property to solve for x.

It factors into (x - 14)( x - 2 ) = 0, and so the values for x are 14 or 2. For each value of "x", we need to find the corresponding value of " x+2 ". So when x = 14, x+2 would equal 16. When x = 2, x+2 would equal 4.

If we check both of these sets of consecutive even integers in the original equation, we find that both sets of numbers work, so the two consecutive even integers are either 14 and 16 or 2 and 4.