Ratios and proportions help needed

Pimptatay said:
This doesn’t make sense either. How did you come up with 18 and 66 lol
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@Pimptatay, The idea is to divide \(\displaystyle 84\) into \(\displaystyle 11+3=14\) parts.
Then we need \(\displaystyle 3\) parts and then \(\displaystyle 11\) parts, where each part is \(\displaystyle \tfrac{1}{14}\) of \(\displaystyle 84\).
So please when you get a reply from a real mathematician don't be a dumb ass.
 
pka said:
@Pimptatay, The idea is to divide \(\displaystyle 84\) into \(\displaystyle 11+3=14\) parts.
Then we need \(\displaystyle 3\) parts and then \(\displaystyle 11\) parts, where each part is \(\displaystyle \tfrac{1}{14}\) of \(\displaystyle 84\).
So please when you get a reply from a real mathematician don't be a dumb ass.
Click to expand...

You’re right I’m sorry. I was getting frustrated as you can tell. I’m a physical thinker rather than words.
 
I don't think you are really understanding the question. I'm going to take you back to basics. Picture this.
You have 84 buttons and you have to put them into two tins such that the ratio of the buttons in the tins is 3:11. In other words, for every 3 buttons you put in tne first tin, you have to put 11 buttons in the second tin. Ok so, imagine you put 3 buttons in Tin A and 11 buttons in Tin B. Have you used up all the buttons? No, so do it again.
Now you have 6 buttons in Tin A and 22 buttons in Tin B. Right? Have you used up all the buttons? No, you've only used 28 buttons. So, do it again etc:
Tin A: 9 Tin B: 33 (only used 42 buttons)
Again:
A: 12 B: 44
A: 15 B: 55
A: 18 B: 66 Have you used all the buttons now? YES

So to split the 84 buttons in the ratio 3:11, you need 18 in one pile and 66 in the other.

That's the long way, but that's what's happening.

Here's the short way.
3+11=14
3/14 of the 84 buttons = 3/14 × 84 =18
11/14 × 84 = 66.
 
That
Harry_the_cat said:
I don't think you are really understanding the question. I'm going to take you back to basics. Picture this.
You have 84 buttons and you have to put them into two tins such that the ratio of the buttons in the tins is 3:11. In other words, for every 3 buttons you put in tne first tin, you have to put 11 buttons in the second tin. Ok so, imagine you put 3 buttons in Tin A and 11 buttons in Tin B. Have you used up all the buttons? No, so do it again.
Now you have 6 buttons in Tin A and 22 buttons in Tin B. Right? Have you used up all the buttons? No, you've only used 28 buttons. So, do it again etc:
Tin A: 9 Tin B: 33 (only used 42 buttons)
Again:
A: 12 B: 44
A: 15 B: 55
A: 18 B: 66 Have you used all the buttons now? YES

So to split the 84 buttons in the ratio 3:11, you need 18 in one pile and 66 in the other.

That's the long way, but that's what's happening.

Here's the short way.
3+11=14
3/14 of the 84 buttons = 3/14 × 84 =18
11/14 × 84 = 66.
Click to expand...
Thank you!!!
Now that created an image in my head.
I am stupid. I’m sorry folks.
 
Pimptatay said:
That
Thank you!!!
Now that created an image in my head.
I am stupid. I’m sorry folks.
Click to expand...
No, you're not stupid!! A stupid person wouldn't ask the question in the first place! The best way to learn is to continue asking questions!!
 
Say if it were to change the numbers say:
“Divide 400 in two (2) parts in the ratio 4:16.” (Just made up the numbers)

Theoretically: 4x+16x=400
20x=400
X=20

Therefore,
4/20 of 400/1 = 1600/20 =80
16/20 of 400/1 = 6400/20 = 320
80+320 =400
 
Ok, let's calm down. I will give it a try. BTW you almost had it!

The ratio of 3:11 is equivalent 6:22 or 9:33 or 30:110. That is any ratio in the form of 3x:11x is the same as 3:11. Now we are dividing the 84 into two parts (that sum to 84). One part is 3x and the other part is 11x--remember this makes sense because we want to keep that ratio as 3:11.

The two parts add to 3x+11x or 14x. But this sum, 14x, must equal 84. That is 14x=84 and x=6
But remember that the two parts are 3x and 11x, better known as 18 and 66. Please note that 18:66 reduces to 3:11 and 18+66=84!
 
you want the ratio of \(\displaystyle \dfrac{3}{11}\)

this is the same as \(\displaystyle \dfrac{\dfrac{3}{3+11}}{\dfrac{11}{3+11}}=\dfrac{\dfrac{3}{14}}{\dfrac{11}{14}}\)

So the first part gets \(\displaystyle \dfrac{3}{14} \cdot 84 = 18\)

and the second part gets \(\displaystyle \dfrac{11}{14} = 66\)

You do this normalization so that your two portions equal the entire batch.
 
Romsek said:
you want the ratio of \(\displaystyle \dfrac{3}{11}\)

this is the same as \(\displaystyle \dfrac{\dfrac{3}{3+11}}{\dfrac{11}{3+11}}=\dfrac{\dfrac{3}{14}}{\dfrac{11}{14}}\)

So the first part gets \(\displaystyle \dfrac{3}{14} \cdot 84 = 18\)

and the second part gets \(\displaystyle \dfrac{11}{14} = 66\)

You do this normalization so that your two portions equal the entire batch.
Click to expand...

This makes sense too, but now it’s again getting too complicated to what was suppose to be a simple equation.
 
You want to break up 45 into 10 equal pieces. Since 45/10 =4.5, each piece is 4.5
Someone gets 3 pieces---------4.5*3 = 13.5
Someone else gets 7 pieces----4.5*7= 31.5
 
Harry_the_cat said:
"Divide 45 in the ratio 3:7" is NOT asking you to divide 3/7 by 45.
You nearly had it before. Look back at post #26&27.

3+7=10
One pile gets 3/10 of 45, the other gets 7/10 of 45.
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Okay now I’m confused again.
Why is the wording problem so complicated.
I cannot wrap my head around the idea. I get but it doesn’t make sense to my dumb head.
 
Jomo said:
You want to break up 45 into 10 equal pieces. Since 45/10 =4.5, each piece is 4.5
Someone gets 3 pieces---------4.5*3 = 13.5
Someone else gets 7 pieces----4.5*7= 31.5
Click to expand...

I get that the “10” comes from adding 3+7. But, how do you just add the ratio of something to get ratio of x:45
 
Jomo said:
You want to break up 45 into 10 equal pieces. Since 45/10 =4.5, each piece is 4.5
Someone gets 3 pieces---------4.5*3 = 13.5
Someone else gets 7 pieces----4.5*7= 31.5
Click to expand...

This is somewhat making sense to me. The party that “you want to break up 45 into 10 equal pieces” is what I’m confused with.

I get the calculation but how do you just derive to 10 all the sudden.

The ratio was 3:7 so what you just add those for no reason?? To get whatever you need to split the 45?
 
Romsek said:
you want the ratio of \(\displaystyle \dfrac{3}{11}\)

this is the same as \(\displaystyle \dfrac{\dfrac{3}{3+11}}{\dfrac{11}{3+11}}=\dfrac{\dfrac{3}{14}}{\dfrac{11}{14}}\)

So the first part gets \(\displaystyle \dfrac{3}{14} \cdot 84 = 18\)

and the second part gets \(\displaystyle \dfrac{11}{14} = 66\)

You do this normalization so that your two portions equal the entire batch.
Click to expand...
This might have something to do with it
 
Imagine this or actually draw it better still.
Draw a line 10 inches long. Mark a point 3 inches from one end.
The point divides the line in the ratio 3:7. Right?
The smaller part is 3/10 of the line.
The bigger part is 7/10 of the line.
 
Pimptatay said:
This is somewhat making sense to me. The party that “you want to break up 45 into 10 equal pieces” is what I’m confused with.

I get the calculation but how do you just derive to 10 all the sudden.
Click to expand...
It's the same idea that causes you to divide something into 2 parts when you share equally with a friend. You are dividing so that the ratio is 1:1. And 1+1=2.
If you want the friend to have twice as much, the ratio would be 1:2 and you would divide into 3 parts. The friend gets 2 of them and your get 1.
 
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