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The school that Lisa goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold S adult tickets and 3 child tickets for a total of $100. The school took in $37 on the second day by selling 2 adult tickets and 1 child ticket. What is the price each of one adult ticket and one child ticket?

User Xorsat
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Let x represent the price of one adult ticket

Let y represent the price of one child ticket

We were told that on the first day of ticket sales, the school sold 5 adult tickets and 3 child tickets. The cost wof these tickets would be 5x + 3y

Given that the total amount was $100, it means that

5x + 3y = 100

Also, the school took in $37 on the second day by selling 2 adult tickets and 1 child ticket. This would be expressed as

2x + y = 37

y = 37 - 2x

If we substitute y = 37 - 2x into 5x + 3y = 100, it becomes

5x + 3(37 - 2x) = 100

5x + 111 - 6x = 100

5x - 6x = 100 - 111

- x = - 11

Dividing both sides by - 1, it becomes

x = 11

y = 37 - 2x = 37 - 2 * 11

y = 37 - 22

y = 15

Thus, the cost of one adult ticket is $15 and the cost of one child ticket is $11

User Ali Zarei
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