A concert manager counted 550 ticket receipts the day after a concert. The price for a student ticket was $12.50, and the price for an adult ticket was $16.00. The register confirms that $8,362.50 was taken in. How many student tickets and adult tickets were sold?

Question

Mathematics

Gustavo Andrade

15 October, 22:58

A concert manager counted 550 ticket receipts the day after a concert. The price for a student ticket was $12.50, and the price for an adult ticket was $16.00. The register confirms that $8,362.50 was taken in. How many student tickets and adult tickets were sold?

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Answers (1)

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Hinton · Answer 1

Students ticket = 125

Adults ticket = 425

Step-by-step explanation:

Let Student ticket = S

Adult ticket = A

A + S = 550 ... (1)

The price for a student ticket was $12.50, and the price for an adult ticket was $16.00. The register confirms that $8,362.50 was taken in that is

16A + 12.5S = 8362.5 ... (2)

Solve equation 1 and 2 simultaneously

A + S = 550

16A + 12.5S = 8362.5

Multiply S in equation 1 by 12.5

12.5A + 12.5S = 6875

16A + 12.5S = 8362.5

3.5A = 1487.5

A = 1487.5/3.5

A = 425 tickets

Substitute A in equation (1)

425 + S = 550

S = 550 - 425

S = 125 ticket