The theater sells two types of tickets: adult tickets for $15 and child tickets for $3. Last night, the theater sold a total of 334 tickets for a total of $3342. How many adult tickets did the theater sell last night?

Step-by-step explanation:

An adult ticket will be x.

Each adult ticket costs 15 dollars, so 15x

A child ticket will be y.

Each child ticket costs 3 dollars, so 3y

334 tickets were sold, totaling 3342 dollars.

15x + 3y = 3342 dollars in total.

Unknown number of adult tickets plus unknown number of child tickets equals to 334, so:

x number of adult tickets + y number of child tickets = 334 tickets in total.

x + y = 334

There are two equations in a system.

Use substitution:

x + y = 334

y = 334 - x

And plug it into other equation:

15x + 3(334 - x) = 3342

Solve for x since the question only asked for total number of adult tickets sold at theater (remember x is the number of adult tickets)

15x + (1002 - 3x) = 3342

15x + 1002 - 3x = 3342

Bring all x variables to one side and constants to other side:

15x - 3x = 3342 - 1002

12x = 2340

Divide both sides by 12:

x = 195

With that answer, we can conclude that 195 adult tickets were sold at the theater last night!

ANSWER: 195

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