Question

The admission fee at a movie theater is $5 for children and $9 for adults. If 3200 people go to the movies and $24000 is collected, how many adults went to the movies?

Answer 1

Answer:1200

Explanation:

number of adults = a

number of children = c

total number: a + c = 3200

total collected: 9a + 5c = 24000

a + c = 3200 → a = 3200 − c

9a + 5c = 24000

9(3200 − c) + 5c = 24000

c = 1200

Answer 2

For this problem, let x be the number of children and y for adults. Formulate the equations: 1st equation, x + y = 3,200 and 2nd equation 5x + 9y = 24,000. Re-arrange 1st equation into x = 3200 - y. Then, substitute into 2nd equation, 5(3,200-y) + 9y = 24,000. Then, solve for y. The 16,000 - 5y + 9y = 24000. Final answer is, y = 2000 adults went to watch the movie.