Can someone do it the algebra way?Solve Ratio & Proportion Homework: 3:2 to 3:7

[adjacent]

Homework Statement

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!

Homework Equations

nope

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.

 

[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.

 

[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 .

 

[adjacent]

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

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

 

[Tanya Sharma]

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

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

Nevertheless , S doesn't have a unique value.

 

[adjacent]

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

Nevertheless , S doesn't have a unique value.

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.

 

[haruspex]

So what do you mean by substituting the value of S?Does that mean using any number or substituting 3x+2x?

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

 

[PeroK]

Homework Statement

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?

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

 

[HallsofIvy]

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.

 

[Tanya Sharma]

So what do you mean by substituting the value of S?Does that mean using any number or substituting 3x+2x?

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

Sorry I am a bit off because of the Chemistry test tomorrow.

All the Best !

 

[adjacent]

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

 

[adjacent]

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.

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

 

[Dick]

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

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.

 

[adjacent]

Thank you.It's clear now