Question

A theater wants to take in at least $2000 for a certain matinee. Children's tickets cost $5 each and adult tickets cost $10 each. The theater has a maximum of 350 seats.

Answer 1

The correct answer is x + 2y
`\geq` 400 and also y
`\geq 50` and x
`\leq 300`.

Explanation:

Amount a theater wants for a certain matinee = $2000

Cost of Children's ticket is $5 and for adult is $10.

Let there are x children and y adults in the theater. Total capacity of the theater is maximum 350. Thus x + y
`\leq` 350.

Thus the above situation can be demonstrated as:

5x + 10y
`\geq` 2000

⇒ x + 2y
`\geq` 400 and also y
`\geq 50` and x
`\leq 300`.

Thus the set of solutions can be given by the above three inequalities. One such possibility could be 300 students and 50 adults for the matinee.