SOLUTION: If 120 people paid a total of $120.00 to attend a party where men paid $5.00, women paid $2.00 and children paid .10, how many of each attended the party?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If 120 people paid a total of $120.00 to attend a party where men paid $5.00, women paid $2.00 and children paid .10, how many of each attended the party?      Log On


   

Question 1014745: If 120 people paid a total of $120.00 to attend a party where men paid $5.00, women paid $2.00 and children paid .10, how many of each attended the party?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let m = # of men who attended, w = # of women who attended, and c = # number of children who attended.
Then
m + w + c = 120, and
5m + 2w + 0.10c = 120.
Substituting c = 120 - m - w into the second equation, we get
5m + 2w + 0.10(120 - m - w) = 120, which, after simplifying, gives
4.9m + 1.9w = 108, or
49m + 19w = 1080. This becomes a Diophantine problem, and as such requires (non-negative) integer solutions.
By brute force, we obtain m = 17 and w = 13, from which we get c = 90.
(These values can also be obtained using the Euclidean algorithm.)
Thus, there were 17 men, 13 women, and 90 children.