Word problem with factoring

Question

One number is 2 more than 2 times another. Their product is 24. Find the numbers.

I need four answers

Answer 1

Let x = first unknown number.

Since you are told "one number is 2 more than 2 times another", this means the second unknown number can be written as 2x + 2.

You are told the produce is 24, so you would get the equation x(2x+2) = 24 and you need to solve this.

x(2x + 2) = 24

2x^2 + 2x = 24

2x^2 + 2x - 24 = 0

2(x^2 + x - 12) = 0

2(x + 4)(x - 3) = 0

x + 4 = 0 or x - 3 = 0

x = -4 or x = 3

If x = -4, then the other number is 2(-4) + 2 = -6. So you get one pair of -4 and -6.

If x = 3, then the other number is 2(3) + 2 = 8. So you get a second pair of 3 and 8.