For the opening night of a school play, a total of 320 tickets were sold, raising a total … — ACT

For the opening night of a school play, a total of $320$ tickets were sold, raising a total of $\$2{}140$ in ticket sales. Student tickets were sold for $\$5$ each, and adult tickets were sold for $\$8$ each. How many adult tickets were sold?

Answer: 180

Answer

180

The correct answer is

180

. By setting up a single-variable linear equation where

a

represents the number of adult tickets, the problem translates to

8a + 5(320 - a) = 2140

. Simplifying this yields

3a + 1600 = 2140

, which simplifies to

3a = 540

and results in

a = 180

Step-by-Step Solution

Define variables for the unknown quantities based on the given total.

Let

a

represent the number of adult tickets sold. The number of student tickets sold is represented as

320 - a

Since the total number of tickets is

320

, subtracting the number of adult tickets from the total yields the number of student tickets.

Construct a linear equation using the ticket prices and the total revenue.

8a + 5(320 - a) = 2140

Multiplying the quantity of each ticket type by its respective price (

8

dollars for adult and

5

dollars for student) yields the total ticket sales revenue of

2,140

dollars.

Solve the equation for the variable

a

8a + 1600 - 5a = 2140 \implies 3a + 1600 = 2140 \implies 3a = 540 \implies a = 180

Apply the distributive property, group like terms, isolate the variable term, and divide to solve for the number of adult tickets.

Key Concept

Translating word problems into a single-variable linear equation and solving for the unknown quantity.

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