The ratio between three numbers is:
Three and one third: Four and one fifth: Six and one eighth and the sum of the numbers is $4197$. What are the three numbers?
Using a calculator, I would just add up the numbers which equals $13\frac{79}{120}$, divide $4197$ by $13\frac{79}{120}$ and then multiply each of the numbers in the ratio by that answer.
Without a calculator, the arithmetic seems impossible, or is there an easier way?
The simplified ratio is as follows: $$\frac{10}{3}:\frac{21}{5}:\frac{49}{8}$$ $$400:504:735$$
You can find the actual numbers by using the above ratio and the sum of the numbers.
$$400x+504x+735x = 4197$$ $$x = \frac{4197}{1639}$$