MHB Total Profit of the business partners for the year

[mathdad]

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?

 

[Wilmer]

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?!

 

[HOI]

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)

 

[mathdad]

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