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Chapter 2: Q. 260 (page 164)

Last Saturday, the museum box office sold 281 tickets for a total of \(3,954. Adult tickets cost \)15and student tickets cost $12. How many of each kind of ticket was sold?

Short Answer

Expert verified

There are 194 adult tickets and 87 student tickets.

Step by step solution

01

Given information

Last Saturday, the museum box office sold 281 tickets for a total of $3,954. Adult tickets cost $15 and student tickets cost $12.

02

Determine the linear equation.

Let the number of $15Adult tickets be x.

The cost of $15adult tickets be:

15x

Let the number of $12student tickets be y.

The cost of $12student tickets be:

12y

Since the total price is $3954, make an equation:

15x+12y=3954

There are total 281tickets. Therefore, the equation becomes:

x+y=281

Solve x+y=281for x.

x=281-y

03

Determine number of $12 adult tickets

Substitute 281-yfor xin 15x+12y=3954.

15281-y+12y=39544215-15y+12y=3954-3y=-261y=2613=87

04

Determine the number of $15 student tickets

Substitute 87for xin x=281-y.

x=281-87=194

05

Write the conclusion

Therefore, the number of $12adult tickets and $15student tickets are87and194respectively.

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