# 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?

Dec 5, 2016

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:

$2 n = 3 m + 15$

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

$2 \left(m - 4\right) = 3 m + 15$

$2 m - 8 = 3 m + 15$

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

$- 8 - 15 = 3 m - 2 m$

$- 23 = m$

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

$n = - 23 - 4$

$n = - 27$