For a special show, the Grand Apollo Theater charged ticket prices as follows: adults, $10; students, $3; and children under 12, 50 cents. The theater collected a total of $100 from an audience of 100 people. How many adults, students, and children were in the audience?
Let’s let a represent the number of adults and s, the number of students. Then:
10a + 3s + (100 – a – s)(.5) = 100
10a + 3s + 50 – .5a – .5s = 100
9.5a + 2.5s = 50
Trying small numbers (1, 2, …) for a and s, we find that a = 5 and s = 1 is the first integer solution that works.
Check: 5(10) + 1(3) + 94(.5) = 50 + 3 + 47 = 100.