could someone help with this?

Question

One number is 2 more than 2 times another. Their product is
40 Find the numbers.

 

Their numbers are _______ and _______ or ________ and _______ 

 

Answer 1

Let x = 1st number

 

     2x + 2 = the other number

 

 

Their product is 40. So, (2x + 2)x = 40

 

Multiply (2x + 2) and x and get 2x² + 2x = 40

 

2x² + 2x - 40 = 0

 

Factor it out. The factors are (2x + 10) and (x - 4).

 

(2x + 10) (x - 4) = 0

 

Find the roots.

 

a) 2x = -10

      x = -10/2 = -5

 

    Solve the other number using x = -5

 

    2x + 2

    2(-5) + 2 = -10 + 2 = -8

 

Then the first pair of numbers is (-5,-8)

 

b)  x - 4 = 0
         x = 4

Solve the other number using x = 4

2x + 2
2(4) + 2 = 8 + 2 = 10

 

Then the second pair of numbers is (4,10)