Answer:
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
