Question

One number is seven less than a second number. Twice the first is 10 more than 6 times the second. How do you find the numbers?

Answer 1

The first number is `-13` and the second number is `-6`

Explanation:

Let's let the first number be `n` and the second number be called `m`.

Then, from the first sentence we can write:

`n = m - 7`

and from the second sentence we can write:

`2n = 6m + 10`

Substitute `m - 7` for `n` in the second equation and solve for `m`:

`2(m - 7) = 6m + 10`

`2m - 14 = 6m + 10`

`2m - 14 - 2m - 10 = 6m + 10 - 2m - 10`

`-14 - 10 = 6m - 2m`

`-24 = 4m`

`(-24)/4 = (4m)/4`

`m = -6`

Now substitute `-6` for `m` in the first equation and calculate `n`:

`n = -6 - 7`

`n = -13`