Question 1167081
let m = the number of men
let w = the number of women.


your ratio is m/w = 5/6


solve for m to get m = 5/6 * w


you are given that there are 150 more women then men.


this leads to w = m + 150


in the equation of m = 5/6 * w, replace w with m + 150 to get m = 5/6 * (m + 150)
multiply both sides of the equation by 6 to get 6m = 5 * (m + 150).
simplify to get 6m = 5m + 750.
subtract 5m from both sides of the equation and simplify to get m = 750.


since the ratio of men to women is 5/6, then the ratio becomes 750/w = 5/6
multiply both sides of that equation by w to get 750 = 5/6 * w
solve for w to get w = 6/5 * 750 = 900.


you have the number of men = 750 and the number of women = 900 for a total enrollment of 1650 at the college.