Question

One number is four less than a second number. Twice the first is 15 more than 3 times the second. How do you find the numbers?

Answer 1

The two numbers are `-23` and `-27`

Explanation:

We need to first write this problem in terms of equation and then solve the simultaneous equations.

Let's call the numbers we are looking for `n` and `m`.

We can write the first sentence as an equation like:

`n = m - 4`

And the second sentence can be written as:

`2n = 3m + 15`

Now we can substitute `m - 4` into the second equation for `n` and solve for `m`;

`2(m - 4) = 3m + 15`

`2m - 8 = 3m + 15`

`2m - 2m - 8 - 15 = 3m - 2m + 15 - 15`

`-8 - 15 = 3m - 2m`

`-23 = m`

We can now substitute `-23` for `m` in the first equation and calculate `n`:

`n = -23 - 4`

`n = -27`