How would you solve this problem using guess and check, and then algebraically?

Here is the problem:





There are nine men to every ten women at Big State U. There are 26,239 students at the university. How many women are there?





I solved it using a diagram and got 12,332 men, and 13,907 women, but I need to solve it using guess and check, and then again algebraically. Any ideas?|||Algebraically:





Let m = number of men, w the number of women





w+m = 26239





10m = 9w or w = (10/9) m





m + (10/9)m = 26239





m = (9/19) 26239 = 12429





w = 26239 - 12429 = 13810|||are you kidding ? its a proportion problem, not guess and check, not algebraically.


your solutions are wrong.