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a concert manager counted 650 ticket receipts the day after a concert. the price for a student ticket was $11.50, and the price for an adult ticket was $13.00. the register confirms that $8,112.50 was taken in. how many student tickets and adult tickets were sold?

Respuesta :

Lanuel

Based on the calculations, the number of student tickets and adult tickets that were sold are 225 tickets and 425 tickets respectively.

Given the following data:

Total ticket receipts = 650 tickets.

The price for a student ticket = $11.50.

The price for an adult ticket = $13.00.

Total revenue = $8,112.50.

  • Let T represent the total ticket.
  • Let S represent price for a student ticket.
  • Let A represent price for an adult ticket.
  • Let R represent the total revenue.

What is an expression?

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

How many student tickets and adult tickets were sold?

In order to determine the number of student tickets and adult tickets that were sold, we would translate the word problem into an algebraic expression as follows:

A + S = 650                              ......equation 1.

11.5S + 13A = 8,112.50              ......equation 2.

From eqn. 1, we have:

S = 650 - A                          ......equation 3.

Substituting eqn. 3 into eqn. 2, we have:

11.5(650 - A) + 13A = 8,112.50

7,475 - 11.5 A + 13A = 8,112.50

1.5A = 8,112.50 - 7,475

1.5A = 637.5

A = 637.5/1.5

A = 425 tickets.

For the student tickets, we have:

S = 650 - A

S = 650 - 425

S = 225 tickets.

Read more on expressions and equations here: https://brainly.com/question/15697717

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