# Homework Help: Ratios and Proportions

1. Sep 16, 2010

### zorro

1. The problem statement, all variables and given/known data

Let s-a : s-b : s-c :: 1:2:3

then how do we find a:b:c from this?

2. Relevant equations

3. The attempt at a solution

2. Sep 16, 2010

### Staff: Mentor

Try to format your expression in such a way that it is unambiguous what you are looking for.

3. Sep 16, 2010

### zorro

How do I do that?

4. Sep 16, 2010

### Staff: Mentor

5. Sep 16, 2010

### Staff: Mentor

Rewrite this proportion as three equations. The proportion is saying is that s - b is 2 times s - a, s - c is 3 times s - a, and s - c is (3/2) times s - b.

That should give you somewhere to start.

6. Sep 16, 2010

### zorro

Thanks alot

7. Sep 16, 2010

### HallsofIvy

That's slightly confusing because it represents several proportions together.
You can analyze it as $s-a: s-b::1:2$, $s-b: s-c::2: 3$, and [itex]s-a: s-c::1: 3[itex]. Those can be written as fraction:
$$\frac{s-a}{s-b}= \frac{1}{2}$$
$$\frac{s-b}{s-c}= \frac{2}{3}$$
and
[tex]\frac{s-a}{s-c}= \frac{1}{3}

The first equation can be rewritten as 2(s- a)= s- b, 3(s-b)= 2(s- c), and 3(s-a)= s- c.

You can solve each of those for s: 2s- 2a= x- b so s= 2a- b. 3s- 3b= 2s- 2c so s= 3b- 2c. 3s- 3a= s- c so 2s= 3a- c or s= (3/2)a- (1/2)c.

Now put them back together: s= 2a- b= (2/3)a- (1/2 c, s= 2a- b= 3b- 2c. You should be able to find the relationships between a, b, and c from that.

8. Sep 16, 2010