Question

A dinner was held to raise money for a children's museum. A ticket for one person cost $200 and a ticket for a couple (two people) cost $350. A total of 130 people attended the dinner, and the ticket sales total was $24,000. What is the total number of tickets that were sold?

Answer 1

90 tickets

Explanation:

Given that 130 people bought single tickets for $200 or couple tickets for $350, and total ticket revenue was $24,000, you want the total number of tickets sold.

Setup

We could figure the number of each kind of ticket sold, but we choose to solve directly for the total number of tickets, n. The number of people was ...

s + 2c = 130

and the number of tickets was ...

s + c = n

so, the number of couples was ...

c = 130 -n

and the number of singles was ...

s = n - c = n - (130 -n) = 2n -130

The revenue equation is ...

200(2n -130) +350(130 -n) = 24000

Solution

400n -26000 +45500 -350n = 24000 . . . . eliminate parentheses

50n +19500 = 24000 . . . . . . . . collect terms

50n = 4500 . . . . . . . . . . . subtract 19500

n = 90 . . . . . . . . . . divide by 50

The total number of tickets sold was 90.

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Additional comment

The attachment shows the solution for the individual numbers of single (50) and couples (40) tickets sold. The sum of those is 90, as above.

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