# How do you solve ratio problems like these?

## Homework Statement

In each of the following the properties of a compound are given. In each case find A:B:C

1. 1/5 of A, 2/3 of B and the remainder of C.

2. 3/8 of A with B and C in the ratio 1:2.

3. A, B and C are mixed according to the ratios A:B= 2:5 and B:C=10:11.

## The Attempt at a Solution

I could only solve the 1st one:

The common denominator is 15 so 15/3*2=10 and 15/5*1=3. That means A and B are in the ratio 3:10.

15/15-13/15=2/15 so A:B:C are in the ratio of 10:3:2

Couldn't solve the other two. Please, help. Thanks.

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uart
Ok in Q2 you know that the remainder (B and C) make up 5/8. Can you show how to split 5/8 in the ratio 1:2?

Regarding Question 1:

I think you got the answer right but in the wrong order.

$A:B:C$

$\frac{1}{5}:\frac{2}{3}:\frac{x}{y}$

$(\frac{3}{15}:\frac{10}{15}:\frac{2}{15})*15$

$3:10:2 == A:B:C$

Regarding Question 2:
You need the provided fraction to become large enough that it's remainder is evenly divisible into three parts.

Regarding Question 3:
A:B:C is what you're trying to build, so look at the ratios A:B and B:C as puzzle pieces.
A:B is too small to fit in with B:C, so you simply need to make A:B larger for it to be congruent with B:C

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