# Ratio and proportion

1. Feb 15, 2014

1. The problem statement, all variables and given/known data
A man and a women share a sum of money in the ratio 3:2. If the sum of money is doubled ,in what ratio should they divide it so that the man still receives the same amount?

Just a gr.8 problem.Forgive me!

2. Relevant equations
nope

3. The attempt at a solution
What I couldn't do is the algebra way.Can someone do it the algebra way?
This is what I did:
$\frac{3}{5}*x=y$

$\frac{z}{5}*2x=y$

So I just made $x$, 100 and $2x$ is 200,obviously.
$\frac{3}{5}*100=60$
so I found the z which is 1.5
Then: $x$ is something else here.
1.5 ---> 60
x ---> 200-60(140)
So ratio is $1.5:3.5$
Which can also be written as $3:7$
I got the answer.But I want to do it the right way.

Last edited: Feb 15, 2014
2. Feb 15, 2014

### voko

I cannot follow your solution. I would start by introducing the following variables: x, y, z: man's money, woman's money, sum - all before doubling. X, Y, Z - ditto, after doubling. Then write equations relating all those.

3. Feb 15, 2014

### Tanya Sharma

A more systematic way can be :

Let S denote the sum and 'x' be the constant of proportionality .Then the amount man and woman have is 3x and 2x respectively .

3x + 2x = S

When the amount is doubled ,man still receives the same amount 3x .Let woman receive 'y' amount .

3x+y = 2S

Substituting the value of S from first equation into second will give you 'y' . That will give you the new ratio .

4. Feb 15, 2014

How do we know the value of S?It can be any sum

5. Feb 15, 2014

### Tanya Sharma

You are required to find the new ratio , not S .

Nevertheless , S doesn't have a unique value.

6. Feb 15, 2014

So what do you mean by substituting the value of S?Does that mean using any number or substituting 3x+2x?
Sorry I am a bit off because of the Chemistry test tomorrow.

7. Feb 15, 2014

### haruspex

Yes. Tanya meant "substitute the expression for S".

8. Feb 15, 2014

### PeroK

I would just do it like this:

Let the initial sum be 5x. The man gets 3x, the woman 2x.

The sum is doubled, so now 10x. The man still gets 3x and the woman 7x.

So, the new ratio is 3:7

9. Feb 15, 2014

### HallsofIvy

Staff Emeritus
I wouldn't have bothered with the "x"! Ratio is 3:2 so use 3+ 2= 5. Doubling that gives 10 and the man still gets 3 so the woman gets 10- 3= 7. Ration 3:7.

10. Feb 15, 2014

### Tanya Sharma

Yes. Substitute S=5x from the first eq into the second one. You will get the value of 'y' .

All the Best !

11. Feb 16, 2014

Thank you everyone,Tanya.
HallsofIvy,that's a clever idea.

12. Feb 16, 2014

That doubles the ration not the sum.That was the problem.
However,this approach is also correct.Can you explain a bit?

13. Feb 16, 2014

### Dick

Halls is picking a particular example that solves the problem. 3+2=5 divides 5 in the ratio of 3:2. If you double the 5 and leave 3 fixed then you get 3+?=10. Solving for ? gives you 7. You could also put the x's back in if you don't want to work with a particular example, as PeroK did, 3x+2x=5x. Doubling the total and leaving the 3x fixed gives you 3x+?=10x. So ? is 7x. Same thing.

Last edited: Feb 16, 2014
14. Feb 16, 2014