Chapter 2: Q. 260 (page 164)

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

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$ .

Determine the linear equation.

Let the number of $$ 15$ Adult tickets be $x$ .

The cost of $$ 15$ adult tickets be:

$15 x$

Let the number of $$ 12$ student tickets be $y$ .

The cost of $$ 12$ student tickets be:

$12 y$

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

$15 x + 12 y = 3954$

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

$x + y = 281$

Solve $x + y = 281$ for $x$ .

$x = 281 - y$

Determine number of $12 adult tickets

Substitute $281 - y$ for $x$ in $15 x + 12 y = 3954$ .

$\begin{array}{rcl} 15 (281 - y) + 12 y & = & 3954 \\ 4215 - 15 y + 12 y & = & 3954 \\ - 3 y & = & - 261 \\ y & = & \frac{261}{3} \\ = & 87 \end{array}$

Determine the number of $15 student tickets

Substitute $87$ for $x$ in $x = 281 - y$ .

$\begin{array}{rcl} x & = & 281 - 87 \\ = & 194 \end{array}$

Write the conclusion

Therefore, the number of $$ 12$ adult tickets and $$ 15$ student tickets are $87$ and $194$ respectively.

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

Short Answer

Step by step solution

Given information

Determine the linear equation.

Determine number of $12 adult tickets

Determine the number of $15 student tickets

Write the conclusion

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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

Step by step solution

Given information

Determine the linear equation.

Determine number of $12 adult tickets

Determine the number of $15 student tickets

Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

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