Question

When you take my value and multiply it by -8, the result is an integer greater than -220. If you take the result and divide it by the sum of -10 and 2, the result is my value. I am a rational number. What is my number?

Answer 1

Your value is any rational number greater than `27.5`, or `55/2`.

Explanation:

We can model these two requirements with an inequality and an equation. Let `x` be our value.

`-8x > -220`

`(-8x) / (-10 + 2) = x`

We will first attempt to find the value of `x` in the second equation.

`(-8x) / (-10 + 2) = x`

`(-8x)/-8 = x`

`x = x`

This means that regardless of the initial value of `x`, the second equation will always be true.

Now to work out the inequality:

`-8x > -220`

`x < 27.5`

So, the value of `x` is any rational number greater than `27.5`, or `55/2`.