Total Profit of the business partners for the year

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Discussion Overview

The discussion revolves around the calculation of total profit for three business partners, Q, R, and S, who divide their profits in the ratios of 2:5:8. Participants explore how to set up the equation based on Q's known share of 4,000 and seek clarification on the correct approach to find the total profit.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • Some participants express confusion about how to set up the equation based on the given ratios and Q's share.
  • One participant suggests that the equation 2x + 5x + 8x = 4000 is incorrect, arguing that it does not represent the total profit but rather the individual shares.
  • Another participant clarifies that if Q's share is 4000, then 2x = 4000 leads to x = 2000, which can then be used to find R's and S's shares.
  • Calculations are presented showing that if x = 2000, then R's share would be 10,000 and S's share would be 16,000.
  • The total profit is calculated as 30,000 based on the individual shares of Q, R, and S.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the initial equation setup, with some arguing it is incorrect while others provide clarification on how to derive the total profit from the ratios. The discussion reflects differing interpretations of the problem.

Contextual Notes

There is a lack of clarity regarding the representation of "x" in the initial equation, and participants express different understandings of how to relate the ratios to the total profit. The discussion does not resolve these ambiguities.

mathdad
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Three business partners, Q, R, and S, agree to divide their total profit for a certain year in the ratios: 2 : 5 : 8, respectively. If Q's share was 4,000, what was the total profit of the business partners for the year?

My Reasoning:

1. The variables listed represent 3 people.
2. The word ratio means that there are fractions involved.

My problem is making enough sense of the words
to help me set up the proper equation. I know that Q's share is 4000. No share data has been given for R and S.

I decided to let x be the total profit that we need to find. I came up with the equation 2x + 5x + 8x = 4000. If this equation is incorrect, why is it wrong?
 
Last edited:
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RTCNTC said:
Three business partners, Q, R, and S, agree to divide their total profit for a certain year in the ratios: 2 : 5 : 8, respectively. If Q's share was 4,000, what was the total profit of the business partners for the year?

My Reasoning:

1. The variables listed represent 3 people.
2. The word ratio means that there are fractions involved.

My problem is making enough sense of the words
to help me set up the proper equation. I know that Q's share is 4000. No share data has been given for R and S.

If I let x be the total profit that we need to find. I came up with the equation 2x + 5x + 8x = 4000. If this equation is incorrect, why is it wrong?
Since Q's share = 4000, then 2x = 4000, so x = 2000 : HOKAY?!
 
RTCNTC said:
Three business partners, Q, R, and S, agree to divide their total profit for a certain year in the ratios: 2 : 5 : 8, respectively. If Q's share was 4,000, what was the total profit of the business partners for the year?

My Reasoning:

1. The variables listed represent 3 people.
2. The word ratio means that there are fractions involved.

My problem is making enough sense of the words
to help me set up the proper equation. I know that Q's share is 4000. No share data has been given for R and S.

If I let x be the total profit that we need to find. I came up with the equation 2x + 5x + 8x = 4000. If this equation is incorrect, why is it wrong?
It's not a matter of it being "incorrect", it simply makes no sense because you haven't said what "x" represents! I suspect you are saying since they are in "ratios: 2: 5: 8", thens if Q is 2 times anything, then R is 5 times that "something" and S is 8 times that something. But then "2x+ 5x+ 8x" is to total or Q, R, and S, not just Q itself. You are told that Q= 4000 NOT the total. If Q is 2x and Q is 4000 then 2x= 4000 so x= 2000. Then R= 5(2000) and S= 8(2000)
 
If x = 2000, then R = 5(2000) or 10,000 and S = 8(2000) or 16,000.

I know that Q's share is 4000.

Let TP = total profit

TP = Q + R + S

TP = 4,000 + 10,000 + 16,000

TP = 4,000 + 26,000

TP = 30,000
 
Last edited:

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