Question

The product of two numbers is 240. The first number is 8 less than the second number. Which equation can be used to find x, the lesser number?

Answer 1

`x(x+8)=240`

Explanation:

We are given that
`x` is the lesser number. Therefore, the larger number, which is 8 larger than
`x`, must be
`x+8`. Our two numbers multiplied are
`x(x+8)`, and they must be equal to 240, as that is given by the question.

Thus,

Equation:
`x(x+8)=240`

Distributive Property:
`x^2+8x=240`

Subtracting both sides by 240:
`x^2+8x-240=0`

Factoring:
`(x+20)(x-12)=0`

Casework:
`x+20=0, x-12=0\\x=-20, x=12`

Answer 2

let's consider the highest number as x,

x + x-8 = 240

2x = 232

x = 116

since, your trying to find the equation, it would be x + x-8 = 240