The product of two consecutive odd numbers equals 55 plus ten times the even number which is between them. Find the even number.

14

Step-by-step explanation:

The product of two consecutive odd numbers equals 55 plus ten times the even number which is between them. Find the even number.

Let the two odd consecutive integer be x and x+2

Let the even number between then be x+1

If the product of two consecutive odd numbers equals 55 plus ten times the even number, then;

(x)(x+2) = 55 + 10(x+1)

Expand

x² + 2x = 55 + 10x + 10

x² -8x -65 = 0

x² - 13x+5x - 65 = 0

x(x-13)+5(x- 13) = 0

(x-13) (x+5) = 0

x = 13 and -5

Since the even number is x + 1

Even number = 13 + 1 = 14