Identify the proportion that would correctly solve the following

eddy2017

eddy2017

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Identify the proportion that would correctly solve the following problem.

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?.
Click to expand...

It is a multiple choice but I will post it if you ask me to.
The profit is 400 dollars to be divided on a ratio
of 5 to 3
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

I'm looking for the amount Chris received which was the smallest one.
I have to form a proportion with this values but I am stuck here,
Any tips?
Thanks,
eddy
 
I'd do what you did. (Though if Chris and Kelly divide it 5:3, I'd have said Chris got the larger amount.) In this approach, x is "one part", and you've found that each "part" is $50.

I would not use a proportion; and if I did, there are probably several ways one could do it, so I don't like the question. We do need to see the choices, in order to know what form they have in mind.

Possibly what they expect is to write Chris' amount as x and Kelly's part as 400 - x, then write a proportion that says Kelly : Chris = 5 : 3.
 
Attaching answer choice
 

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eddy2017 said:
Identify the proportion that would correctly solve the following problem.



It is a multiple choice but I will post it if you ask me to.
The profit is 400 dollars to be divided on a ratio
of 5 to 3
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

I'm looking for the amount Chris received which was the smallest one.
I have to form a proportion with this values but I am stuck here,
Any tips?
Thanks,
eddy
Click to expand...
FIND:

how much will Chris recieve = C​

ASSUME:

how much will Kelly recieve =K​

Given:

Chris and Kelly will divide a profit of $400 dollars in the ratio 5: to 3​
​
C + K = 400 ← Chris and Kelly will divide a profit of $400 .........................................................(1)​
​
C/K = 3/5 ← Chris receives the smaller amount → K = C * 5/3​

Solution:

using 1​
​
C + C * 5/3 = 400​
​
C * (8/3) = 400​
​
3/8 = C/400​

Choices:
1641237807682.png

.....................................Now choose your poison.......................
 
Last edited by a moderator:
There are [imath]5+3=\large 8[/imath] parts. Chris gets three parts and Kelly gets five.
 
pka said:
There are [imath]5+3=\large 8[/imath] parts. Chris gets three parts and Kelly gets five.
Click to expand...
Yes, I have already seen that one with ratios where the two ratios are added. Thank you.
which right off the bat will propel me to choose b.
 
Subhotosh Khan said:
FIND:

how much will Chris recieve = C​

ASSUME:

how much will Kelly recieve =K​

Given:

Chris and Kelly will divide a profit of $400 dollars in the ratio 5: to 3​
​
C + K = 400 ← Chris and Kelly will divide a profit of $400 .........................................................(1)​
​
C/K = 3/5 ← Chris receives the smaller amount → K = C * 5/3​

Solution:

using 1​
​
C + C * 5/3 = 400​
​
C * (8/3) = 400​
​
3/8 = C/400​

Choices:
View attachment 30465

.....................................Now choose your poison.......................
Click to expand...
I am studying yours now, parsing it down, taking it all in. there's this addictive magic in seeing Math being unlayered!.
 
Last edited:
eddy2017 said:
Attaching answer choice
Click to expand...
That makes it clear that rather than writing a proportion that is directly equivalent to the problem statement, (400 - x)/x = 5/3, as I suggested, they expect you to first convert the part : part ratio, 5:3, to the part : whole ratios, 5/8 and 3/8.

Or you could take my proportion and add 1 to both sides.

As I said, there are many ways to solve the problem, and questions that give the impression that there is one right way are bad pedagogy.
 
Subhotosh Khan said:
FIND:

how much will Chris recieve = C​

ASSUME:

how much will Kelly recieve =K​

Given:

Chris and Kelly will divide a profit of $400 dollars in the ratio 5: to 3​
​
C + K = 400 ← Chris and Kelly will divide a profit of $400 .........................................................(1)​
​
C/K = 3/5 ← Chris receives the smaller amount → K = C * 5/3​

Solution:

using 1​
​
C + C * 5/3 = 400​
​
C * (8/3) = 400​
​
3/8 = C/400​

Choices:
View attachment 30465

.....................................Now choose your poison.......................
Click to expand...
3/8=x/100
The great 'FIND'!
 
Last edited:
Subhotosh Khan said:
FIND:

how much will Chris recieve = C​

ASSUME:

how much will Kelly recieve =K​

Given:

Chris and Kelly will divide a profit of $400 dollars in the ratio 5: to 3​
​
C + K = 400 ← Chris and Kelly will divide a profit of $400 .........................................................(1)​
​
C/K = 3/5 ← Chris receives the smaller amount → K = C * 5/3​

Solution:

using 1​
​
C + C * 5/3 = 400​
​
C * (8/3) = 400​
​
3/8 = C/400​

Choices:
View attachment 30465

.....................................Now choose your poison.......................
Click to expand...
I dig this setup!
FIND
ASSUME
GIVEN
SOLUTION
 
Subhotosh Khan said:
FIND:

how much will Chris recieve = C​

ASSUME:

how much will Kelly recieve =K​

Given:

Chris and Kelly will divide a profit of $400 dollars in the ratio 5: to 3​
​
C + K = 400 ← Chris and Kelly will divide a profit of $400 .........................................................(1)​
​
C/K = 3/5 ← Chris receives the smaller amount → K = C * 5/3​

Solution:

using 1​
​
C + C * 5/3 = 400​
​
C * (8/3) = 400​
​
3/8 = C/400​

Choices:
View attachment 30465

.....................................Now choose your poison.......................
Click to expand...
I did not follow this step as much as I have racked my brains over it. Don't see it.
using 1

C + C * 5/3 = 400
 
eddy2017 said:
I did not follow this step as much as I have racked my brains over it. Don't see it.
using 1

C + C * 5/3 = 400
Click to expand...

In response #4 What is stated right before I write ............................... C + C * 5/3 = 400
 
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?
 
Subhotosh Khan said:
In response #4 What is stated right before I write ............................... C + C * 5/3 = 400
Click to expand...
using -----1
C + K = 400 ← Chris and Kelly will divide a profit of $400 .........................................................(1)
but do not follow why you wrote the italics for K.

C + C * 5/3 = 400
 
eddy2017 said:
using -----1
C + K = 400 ← Chris and Kelly will divide a profit of $400 .........................................................(1)
but do not follow why you wrote the italics for K.

C + C * 5/3 = 400
Click to expand...
There is no mathematical reason - that bolding and italics was only for emphasis - (sort of like your use of "all CAP" s). Secondary reason is that I have a bold and right leaning mind - Jomo can vouch for it.

Again, that bolding and italics has no mathematical reason.
 
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