How do you do this without using a calculator? The ratio of three numbers is $3\frac{1}{3}:4\frac{1}{5}:6\frac{1}{8}$

Question

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?

See this for math formatting. And I don't see, why the arithmetic is impossible without calculator.:) — quapka, Dec 09 '14 at 11:08
The arithmetic would be 1. Add the fractions. 2. Divide 4197 by that answer. 3. Multiply each fraction in the ratio by that answer. — Little Black Dog, Dec 09 '14 at 11:15

lsp · Answer 1 · 2014-12-09T11:52:01.713

2

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.

$$400x+504x+735x = 4197$$ $$x = \frac{4197}{1639}$$

edited Dec 09 '14 at 11:52

answered Dec 09 '14 at 11:19

lsp

4,745

1

21/5 is correct. – Suzu Hirose Dec 09 '14 at 11:22
I got the simplified ratios by converting the mixed numbers to improper fractions, but then what do I do? – Little Black Dog Dec 09 '14 at 11:23
@little Multiply each of the fractions with 120 – nam Dec 09 '14 at 11:25
1

Oh that makes so much more sense now... Since the LCM is 120 for all of them, I can multiply all the ratios by 120. Thanks :) – Little Black Dog Dec 09 '14 at 11:28
@LittleBlackDog were you able to proceed from where I left and get the result ? – lsp Dec 09 '14 at 11:30

How do you do this *without* using a calculator? The ratio of three numbers is $3\frac{1}{3}:4\frac{1}{5}:6\frac{1}{8}$

1 Answers1

How do you do this without using a calculator? The ratio of three numbers is $3\frac{1}{3}:4\frac{1}{5}:6\frac{1}{8}$