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


Chikis

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

 

30% of y=[math]\frac{30}{100}\times{y}=\frac{3}{10}\times{y}\\\longto\\\frac{3}{10}\times{y}=x\\30% of 3y=\frac{3}{10}\times3y[/math]

What do I make of these?

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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=[math]\frac{30}{100}\times{y}=\frac{3}{10}\times{y}[/math]

[math]\to[/math]

[math]\frac{3}{10}\times{y}=x[/math]

 

30% of 3y =[math]\frac{3}{10}\times3y[/math]

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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121de5b3a00a532e61ba1fde2db88f58-1.png

 

 

 

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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That is

This equation 7d9f6ea532ec84fa685d3bcaa14dcc81-1.png 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.

 

So you rearrange your equation.

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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

[math]\frac{3}{10}\times{x}=x[/math]

[math]\to[/math]

y = 10x/3

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

But why are we multiplying by 3?

Taking 30% of both sides, we have

[math]3y\times\frac{30}{100}=10x\times\frac{30}{100}[/math]

[math]\to[/math]

[math]3y\times\frac{30}{100}=\cancel{10}x\times\frac{3}{\cancel{10}}[/math]

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

[math]\frac{3}{10}\times{x}=y[/math]

[math]\to[/math]

y = 10x/3

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

But why are we multiplying by 3?

Taking 30% of both sides, we have

[math]3y\times\frac{30}{100}=10x\times\frac{30}{100}[/math]

[math]\to[/math]

[math]3y\times\frac{30}{100}=10x\times\frac{3}{10}[/math]

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

Edited by Chikis
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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 [math]\frac{3}{{10}}y = x[/math]

 

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 [math]3y = 10x[/math]

Divide through by three [math]y = \frac{{10}}{3}x[/math]

 

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

 

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

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

[math]\frac{{30}}{{100}}y = x[/math]

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.

[math]\frac{{30}}{{100}}(3y) = 3\left( {\frac{{30}}{{100}}y} \right) = 3(x) = 3x[/math]

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

 

[math]\frac{3}{10}\times{y}=x[/math]

[math]\to[/math]

3y = 10x

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

[math]\therefore[/math]

[math]3y\times\frac{3}{10}=10\times\frac{3x}{10}[/math]

So we can clearly now that

[math]3y\times\frac{3}{10}=3x[/math]

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

For example, I have [math]10\times\frac{3x}{10}[/math], 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 84344e55e5f78091cd26d9fc7bf2b86b-1.png, 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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