A theater had 100 people in the audience consisting of men, women, and children. The ticket prices were: men - $10 each; women - $3 each; children - $0.50 each. The theater collected a total of $100 from 100 people. How many men, women, and children were in the audience?

Question

A theater had 100 people in the audience consisting of men, women, and children.  The ticket prices were:  men - $10 each; women - $3 each; children - $0.50 each.  The theater collected a total of $100 from 100 people.  How many men, women, and children were in the audience?

kinggeorge · Answer

Systems of equations! 

You have 100 people total, so you have $m+w+c=100$ Where $m, w, c$ are the number of men/women/children respectively. Also, $10m+3w+.5c =100$. Try solving for $m, w, c$.

kinggeorge · Answer

You can also use the fact that all of the values must be integers.