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

• adjacent
In summary, the problem involves a man and woman sharing a sum of money in the ratio 3:2. When the sum is doubled, they need to divide it in a certain ratio so that the man still receives the same amount. By using variables and equations, a systematic approach can be used to solve the problem. However, it is also possible to use a particular example to find the new ratio.
adjacent
Gold Member

## 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!

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.

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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.

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 .

Tanya Sharma said:
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

adjacent said:
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.

Tanya Sharma said:
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.

adjacent said:
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".

adjacent said:

## 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

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.

paulmdrdo and adjacent
adjacent said:
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' .

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

All the Best !

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

HallsofIvy said:
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?

adjacent said:
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.

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1 person
Thank you.It's clear now

## 1. Can you explain the concept of ratio and proportion in algebra?

Ratio and proportion are mathematical concepts used to compare quantities and determine their relationship. In algebra, ratio is represented by a colon (:) and proportion is represented by an equal sign (=). Ratios are used to compare two or more quantities of the same kind, while proportions are used to compare quantities of different kinds.

## 2. How do you solve ratio and proportion problems in algebra?

To solve a ratio and proportion problem, you need to set up an equation where the ratios of the given quantities are equal. Then, use cross multiplication to find the missing value. For example, in the ratio 3:2 to 3:7, we can set up the equation 3/2 = x/3 and solve for x.

## 3. What are some real-life applications of ratio and proportion in algebra?

Ratio and proportion are used in a variety of real-life situations, such as cooking and baking, mixing chemical solutions, calculating distances and speeds, and determining ingredient proportions in recipes. They are also used in finance and business, such as calculating interest rates and proportions in financial investments.

## 4. Can you provide some tips for solving ratio and proportion problems in algebra?

One helpful tip is to always label your quantities and use units to keep track of what you are comparing. It is also important to understand the concept of equivalent ratios, as well as how to use cross multiplication to solve for unknown values. Practice is key, so try solving a variety of problems to improve your skills.

## 5. How can I check my work when solving ratio and proportion problems in algebra?

After solving a ratio and proportion problem, you can check your work by plugging the values into the original problem to see if the ratios are equal. You can also solve the problem using a different method, such as using a proportion table or finding the unit rate, to verify your answer.

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