# If 30% of y is equal to x, what, in terms of x, is 30% of 3y?

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If 30% of y is equal to x, what, in terms of x, is 30% of 3y?

30% of y=$\frac{30}{100}\times{y}=\frac{3}{10}\times{y}\\\longto\\\frac{3}{10}\times{y}=x\\30% of 3y=\frac{3}{10}\times3y$

What do I make of these?

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Expressed as a fraction

$30\% ofy = \frac{{30}}{{100}}y$

Can you do it now?

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This is what I had wanted to post before I had a latex error:

If 30% of y is equal to x, what, in terms of x, is 30% of 3y?

30% of y=$\frac{30}{100}\times{y}=\frac{3}{10}\times{y}$

$\to$

$\frac{3}{10}\times{y}=x$

30% of 3y =$\frac{3}{10}\times3y$

What do I make of these?

Edited by Chikis

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Lets express this another way 934x=1000y . Then assume that over time y decreases by about 2-3 a year x 1-2.

Lets assume that x is average female births globally per census figures and y is men born. When guys are young there are more guys than women. However guys tend to die younger. So it's about the same.

If 30% of y is equal to x, what, in terms of x, is 30% of 3y? -> 3

Edited by fiveworlds

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So you have an equation for x in terms of y

So rearrange it to get an equation for y in terms of x

Then multiply what ever this is by 3 to get 3y ie 3 times as much.

Then take 30% of this.

You should notice something interesting about the result.

Edited by studiot

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This equation $\frac{3}{10}\times{y}$ is in terms of what? Is it in terms of x or y?

Edited by Chikis

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That is

This equation is in terms of what? Is it in terms of x or y?

That is not an equation.

You did write an equation out before and I quoted it from your post #3.

Your equation tells you what x is equal to in terms of y.

That is it gives you a way of calculating x if you know y.

What you need is a way of calculating y if you know x.

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That is not an equation.

Sorry, I intended writing

$\frac{3}{10}\times{y}=x$

Am saying in the equation above, what is in terms of what? And why or how we do we know?

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Your equation says what x equals.

So what does y equal?

That is what I mean by rearrange your equation, find what y equals.

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If 30% of y is equal to x, what, in terms of x, is 30% of 3y?

This is an unusually-worded problem.

Did you notice that 30% of 3y = (30/100)∙3∙y = 3∙(30/100)∙y ?
It sounds like you have been studying the Associative Property of Multiplication.
This property means that, because (30/100) and 3 and y are all multiplied together,
you can shuffle them around (that is, "associate" them) in any order.
And knowing that 30% of y = x, — also written as (30/100)∙y = x — then ... (what?)

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So you have an equation for x in terms of y

So rearrange it to get an equation for y in terms of x

Then multiply what ever this is by 3 to get 3y ie 3 times as much.

Then take 30% of this.

You should notice something interesting about the result.

Do you mean

$\frac{3}{10}\times{x}=x$

$\to$

y = 10x/3

multiplyiny by 3, we have 3y = 10x.

But why are we multiplying by 3?

Taking 30% of both sides, we have

$3y\times\frac{30}{100}=10x\times\frac{30}{100}$

$\to$

$3y\times\frac{30}{100}=\cancel{10}x\times\frac{3}{\cancel{10}}$

This gives 30% of 3y in terms of x as 3x.

So you have an equation for x in terms of y

So rearrange it to get an equation for y in terms of x

Then multiply what ever this is by 3 to get 3y ie 3 times as much.

Then take 30% of this.

You should notice something interesting about the result.

Do you mean

$\frac{3}{10}\times{x}=y$

$\to$

y = 10x/3

multiplyiny by 3, we have 3y = 10x.

But why are we multiplying by 3?

Taking 30% of both sides, we have

$3y\times\frac{30}{100}=10x\times\frac{30}{100}$

$\to$

$3y\times\frac{30}{100}=10x\times\frac{3}{10}$

This gives 30% of 3y in terms of x as 3x.

Edited by Chikis

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Chikis post#8

You really must make sure you copy accurately from one line to the next

Chikis post#11

This will make things so much easier.

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It is a bit depressing that pure mathematics - the most esoteric and arcane of studies - is impossible without rigour and an almost obsessive attention to detail.

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You should notice something interesting about the result.

It was, indeed, interesting. That's a really obtusde way to express it though.

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It was, indeed, interesting. That's a really obtusde way to express it though.

I'm sure chikis would be interested in your better way, if you told us what that was.

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I'm sure chikis would be interested in your better way, if you told us what that was.

No, I meant the problem as stated as compared to the solution. But that's usually the case when you're dealing with math.

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No, I meant the problem as stated as compared to the solution. But that's usually the case when you're dealing with math.

Well personally I would not have tackled it this way, but I was concerned to make chikis method work out, rather than attempt to impose my own.

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I'm sure chikis would be interested in your better way, if you told us what that was.

Yes, oh! Am intrested in knowing or getting a better way to express it. Edited by Chikis

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For the record here is the complete solution using the method chikis and I were developing.

Express the statement as an equation $\frac{3}{{10}}y = x$

This is an equation expressing x as a function of y. We want an equation expressing y as a function of x so rearrange.

Multiply through by ten $3y = 10x$

Divide through by three $y = \frac{{10}}{3}x$

We now have an equation expressing y as a function of x so multiply it by 3 to get 3y $3y = 3\left( {\frac{{10}}{3}x} \right) = 10x$

Now take 30% of this $\frac{{30}}{{100}}(3y) = \frac{{30}}{{100}}\left( {10x} \right) = 3x$

This gives the answer as 3x.

We can shorten this by noting in the second line that we have 3x, but most will bypass this combining lines 2 and 3.

*******************************************************************************************************************************************************

My alternative method starts in the same place with the equation

$\frac{{30}}{{100}}y = x$

But this time I multiply the y by 3 straight away and then change the order of multiplication of the 30% and the 3 to find the result directly.

$\frac{{30}}{{100}}(3y) = 3\left( {\frac{{30}}{{100}}y} \right) = 3(x) = 3x$

Edited by studiot

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Thanks for voluntering to help. I have reasoned and taught about the problem in a more better way.

30% of y = x

$\frac{3}{10}\times{y}=x$

$\to$

3y = 10x

It is now easier to find 30% of 3y and see what it equals.

$\therefore$

$3y\times\frac{3}{10}=10\times\frac{3x}{10}$

So we can clearly now that

$3y\times\frac{3}{10}=3x$

I want to use this opportunity to ask a question concerning the use of latex to render cancellation.

For example, I have $10\times\frac{3x}{10}$, how do use latex to show that 10 cancelled 10 so that 3x is left.

I mean I want to draw backlash or stroke each on both the 10 at the numerator and denominator respectively to show that. How do I do it? Which code should I use?

Edited by Chikis

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I want to use this opportunity to ask a question concerning the use of latex to render cancellation.

For example, I have , how do use latex to show that 10 cancelled 10 so that 3x is left.

I mean I want to draw backlash or stroke each on both the 10 at the numerator and denominator respectively to show that. How do I do it? Which code should I use?

Sorry I've no idea, but many are following this so perhaps someone else can say.

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Embarassingly enough, I got the wrong answer, so my sublime statement of the problem was obviously just as incorrect as it was neat and tidy. I'll just go back to my corner and be quiet.

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Embarassingly enough, I got the wrong answer

Nice to know there are some other humans on this website.

To err is human ................

I do it all the time.

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