The product of two positive consecutive even integers is 8 more than 4 times their sum. Find the integers

Question

Consecutive Integers Word Problem

Answer 1

let the 1st integer = x

the 2nd integer will be (x + 2)

 

x * (x + 2) = 4[x + (x + 2)] + 8

 

x² + 2x = 4(2x + 2) + 8

 

x² + 2x = 8x + 8 + 8

 

x² + 2x = 8x + 16

 

x² - 6x - 16 = 0

 

(x + 2)(x - 8) = 0

 

The only possible solution is x = 8 because the two integers are positive. Therefore, the first integer is 8, and the second integer is 10.