Solving Ratio problem algebraically

[kapoor.sam]

Hi, can someone show me how to solve the following problem without working backwards by plugging in answer choices?
Problem: A certain college party is attended by both male and female students. The ratio of male to female students is 3 to 5. If 5 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?

[jlucero]

Per forum rules:

2) Cite the source (author or company name) and question number (if applicable) for any problem you post.

[kapoor.sam]

Apologies Joe. This problem is from MGMAT's Advanced Quant guide. Exact problem is on page 40/219 Try-It #2-2

[kapoor.sam]

In any case I got the algebraic expression after discussing with my instructor. Basically the equation to setup is 3x-5/5x=1/2 and then solve for x.

[jlucero]

No worries. We just need to make sure we're not putting copyright material on the forums. Your solution works well and here's another for you:

m/f = 3/5 ---> 5m = 3f

m-5/f = 1/2 ---> 2(m-5) = f

Two unique equations with two variables mean we can solve for one unique set of variables.