A local theater sold a total of 120 tickets for a weekend performance, consisting only of … — GMAT

A local theater sold a total of $120$ tickets for a weekend performance, consisting only of adult tickets and student tickets. Adult tickets were sold for $\$15$ each, and student tickets were sold for $\$10$ each. If the total revenue from the ticket sales was $\$1{}500$ , how many adult tickets were sold?

Answer: 60 tickets

Answer

The correct answer is 60 adult tickets.

By setting up the total ticket equation

a + s = 120

and total revenue equation

15a + 10s = 1500

, substituting

s = 120 - a

gives

15a + 10(120 - a) = 1500

. Simplifying yields

5a = 300

, so

a = 60

. Thus, 60 adult tickets were sold.

Step-by-Step Solution

Set up the linear equation in one variable.

15a + 10(120 - a) = 1500

Express the number of student tickets as

(120 - a)

so the revenue equation relies on a single variable.

Expand and combine like terms.

5a + 1200 = 1500

Distribute

10

across

(120 - a)

to simplify the equation.

Isolate the variable

a

a = 60

Subtract

1200

from both sides and divide by

5

to find the number of adult tickets.

Key Concept

Algebraic Modeling of Linear Systems in Two Variables

Estimated Time:1m 0s

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