Writing Q:R:S = 2:5:8 is concise way or writing the following equations:
Q/R = 2/5
R/S = 5/8
Q/S = 2/8(Also follows from the above two equations)

So if the value of Q is 2, R will be 5 and S will be 8. But, if Q = 4, R will be 10 and S will be 16. Many other such set of values are possible.

To write this in a general fashion, we say that if Q is 2x, R is 5x and S is 8x.
Or,
Q:R:S = 2:5:8 = 4:10:16 = (many other such sets) = 2x:5x:8x

Forget about what is given in the solution, and re-attempt this problem based on what you understand from the explanation given above.

tofubeans wrote:Hello, I need some help understanding the solution to this problem:

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?

The solution solves it by using 2T/(2+5+8) = 4,000 and I'm not sure how/why that is?


PS: Also if any would be so kind to point me to some resources regarding ratios (especially when it's like x:y:z kind of ratios) I'm a little confused by these problems.

Lest apply CFM (Common Factor of Multiplication)method...

=> Q : R : S :: 2:5:8 given,

=> Q : R : S : T :: 2:5:8: (2+5+8); Say T is total profit in ratio scale.

=> Q : R : S : T :: 2:5:8:15;

=> On actual scale Q is 4000, hence cfm for ratio scale is 4000/2 = 2000.

=> So, R = 5 * cfm = 5*2000 = 10000;

=> S = 8 * cfm = 8*2000 = 16000;

=> & T = 15 * cfm = 15*2000 = 30000; Total profit.