Identify the proportion that would correctly solve the following

JeffM said:
Wow Eddy. I recognize that this has already been implied, but let me stress it.

What the Khan of Khans calls the find, I call unknowns. What numbers we not know? TWO NUMBERS : Chris's share and Kelly's shares. Therefore we need two variable names. Not x and the "other x" as you said in your first post. That is missing a critical element of algebra: each unknown is given its own distinct name. Let's use c and k.

Always note exactly but concisely what those names mean.

In your first post, what in the world does x represent? You have not told us. It is a major reason for your problem.

c = what chris gets.

k = what kelly gets.

Do this before you start working on equations. This is part of a systematic way to work on every word problem in algebra.

If you have n unknowns, you need n equations for a numeric solution. Here we have two unknowns so we need two equations.

One is c + k = 400.

What is the other?
Click to expand...
this is what i did in my first post.
The only thing I am thinking right now is to set up two equations with two variables.
5x+ 3x= 400
8x=400
x=50
Replacing the other x with its value.
3(50)=150

So I have two values now
50
And 150
but did not what to do with the two values for x. can you explain following this same reasoning, whaty would you do next?
It was right here that I got stuck. I'm home now at my desktop.
 
eddy2017 said:
this is what i did in my first post.
The only thing I am thinking right now is to set up two equations with two variables.
5x+ 3x= 400
8x=400
x=50
Replacing the other x with its value.
3(50)=150

So I have two values now
50
And 150
but did not what to do with the two values for x. can you explain following this same reasoning, whaty would you do next?
It was right here that I got stuck. I'm home now at my desktop.
Click to expand...
You have not said what x means. 50 and 150 ARE NOT THE ANSWERS REQUESTED.

What does x mean? What does the "other x" mean?

If you have two unknowns you need two distinct variables, like x and y or c and k.

And ALWAYS write down what each variable represents. It will keep you from getting confused, reduces the burden on your memory,, and makes communication easier.
 
eddy2017 said:
this is what i did in my first post.
The only thing I am thinking right now is to set up two equations with two variables.
5x+ 3x= 400
8x=400
x=50
Replacing the other x with its value.
3(50)=150

So I have two values now
50
And 150
but did not what to do with the two values for x. can you explain following this same reasoning, whaty would you do next?
It was right here that I got stuck. I'm home now at my desktop.
Click to expand...
Two values of x? you only have one. x=50.
In your first line, you have 5x +3x=8x = 400. It means that you have a total of 8 parts, 5 parts belong to Chris, and the other 3 belong to Kelly. You figured out each part is worth 50. So how much is Chris' share and how much is Kelly's share?
 
BigBeachBananas said:
Two values of x? you only have one. x=50.
In your first line, you have 5x +3x=8x = 400. It means that you have a total of 8 parts, 5 parts belong to Chris, and the other 3 belong to Kelly. You figured out each part is worth 50. So how much is Chris' share and how much is Kelly's share?
Click to expand...
I don't follow. I am sorry but I must admit I am confused.
what is confusing me is the proportion in the choice. I see it as this:
3/8=x/400

x=50
so replacing the value of x I get 150 so Chris get 150 out of the 400.
but please, BBB, finish with your explanation above. I still haven't fully gotten it.
 
eddy2017 said:
I don't follow. I am sorry but I must admit I am confused.
Click to expand...
Let me put it in another context, maybe it'll help. Suppose a pizza has 8 slices, Chris ate 5 slices, and Kelly ate 3. You found out that each slice cost $50, so how much Chris needs to pay and Kelly needs to pay?
 
I set it up like this. I knew how to start solving it, but then once I got the value of x, i got stumped
3x+5x=400
8x=400
x=50
what does this x value mean for the exercise? I got lost here. let's get back, please.
 
oh, think i see it now
if a share is 50 and the ratio is 5:3
then Kelly gets 250 while Chris gets 150

250 + 150 =400
which is the whole profit.
 
eddy2017 said:
oh, think i see it now
if a share is 50 and the ratio is 5:3
then Kelly gets 250 while Chris gets 150

250 + 150 =400
which is the whole profit.
Click to expand...
I do not know whether you are paying attention to my posts are not.

If you define x as a "share" then the "other x" makes no sense.

You can do it this way. Now you have three variables.

x = share.
c = what Chris gets
k = what Kelly gets

It is c and k that we are interested in.

Three unknowns requires three equations.

c = 3x
k = 5x
c + k = 400

So c + k = 3x + 5x = 8x = 400. Therefore
x = 50.
c = 150.
k = 250.

But you do not need x at all.

c + k = 400.
c/k = 3/5

Because c + k = 400, c = 400 - k.
Thus, (400 - k)/k = 3/5. or 2000 - 5k = 3k
So 8k = 2000.
k = 250.
c = 400 - 250 = 150.

My point is: write down what your variables represent before you start writing equations.
 
JeffM said:
I do not know whether you are paying attention to my posts are not.

If you define x as a "share" then the "other x" makes no sense.

You can do it this way. Now you have three variables.

x = share.
c = what Chris gets
k = what Kelly gets

It is c and k that we are interested in.

Three unknowns requires three equations.

c = 3x
k = 5x
c + k = 400

So c + k = 3x + 5x = 8x = 400. Therefore
x = 50.
c = 150.
k = 250.

But you do not need x at all.

c + k = 400.
c/k = 3/5

Because c + k = 400, c = 400 - k.
Thus, (400 - k)/k = 3/5. or 2000 - 5k = 3k
So 8k = 2000.
k = 250.
c = 400 - 250 = 150.

My point is: write down what your variables represent before you start writing equations.
Click to expand...
This is clearly explained. I see thecwhole process clearly now.
And yes, I need to learn to define the variables appropriately. I like Dr Khan's setup, like I said, but then I lost him. Now I see it quite clearly.
Thank you all.
 
JeffM said:
I do not know whether you are paying attention to my posts are not.

If you define x as a "share" then the "other x" makes no sense.

You can do it this way. Now you have three variables.

x = share.
c = what Chris gets
k = what Kelly gets

It is c and k that we are interested in.

Three unknowns requires three equations.

c = 3x
k = 5x
c + k = 400

So c + k = 3x + 5x = 8x = 400. Therefore
x = 50.
c = 150.
k = 250.

But you do not need x at all.

c + k = 400.
c/k = 3/5

Because c + k = 400, c = 400 - k.
Thus, (400 - k)/k = 3/5. or 2000 - 5k = 3k
So 8k = 2000.
k = 250.
c = 400 - 250 = 150.

My point is: write down what your variables represent before you start writing equations.
Click to expand...
I set up the equation right but did not identify the variables and then got lost.
 
Hello, what an interesting question
Chris and Kelly will divide a profit of $400 400 dollars in the ratio 5: to 3. If Chris receives the smaller amount, how much will Chris recieve?.
Ratios are used to compare two numbers by dividing them. Your formula would be A/ B if you were comparing one data point (A) to another data point (B). This indicates that you are dividing data A by data B.
Here is my approach to solving this question
Let Chris’ amount be x
And Kelly’s amount be y

5 /3 = 400 dollars
Given ratio - 3:5
1 part = 3
2 part = 5
Total no. of parts = 3 + 5 = 8 parts
400 / 8 = 50
3 * 50 = 150
5 * 50 = 250

Since Chris got the smaller amount, he would have 150 dollars
Consequently, Kelly will get 250 dollars

I hope that this calculation helps!
 
JasonTurner said:
Hello, what an interesting question
Chris and Kelly will divide a profit of $400 400 dollars in the ratio 5: to 3. If Chris receives the smaller amount, how much will Chris recieve?.
Ratios are used to compare two numbers by dividing them. Your formula would be A/ B if you were comparing one data point (A) to another data point (B). This indicates that you are dividing data A by data B.
Here is my approach to solving this question
Let Chris’ amount be x
And Kelly’s amount be y

5 /3 = 400 dollars
Given ratio - 3:5
1 part = 3
2 part = 5
Total no. of parts = 3 + 5 = 8 parts
400 / 8 = 50
3 * 50 = 150
5 * 50 = 250

Since Chris got the smaller amount, he would have 150 dollars
Consequently, Kelly will get 250 dollars

I hope that this calculation helps!
Click to expand...
You defined 'x' & 'y' - but did not use those to solve the problem!!!
 
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