# Question #904ae

Aug 3, 2017

24 and 26

#### Explanation:

I derived an equation by using the information given and then used it to calculate the answer via brute force, luckily it only took 2 tries.

We want 12 and 13 to be timed by the same number at the same time.

The ration 12:13 can also be written as $\frac{12}{13}$

So I used that to form the following equation

$\frac{\left(12 \times x\right) - 20}{\left(13 \times x\right) - 20}$

Then subbed in a value for x starting with one and moving up.
You get the answer when you sub in 2.

$\frac{\left(12 \times 2\right) - 20}{\left(13 \times 2\right) - 20} = \frac{2}{3}$