Example 3.29 from Elementary Algebra, 3.3 Solve Mixture Applications

Solve Mixture Applications: example 3.29

At a school concert, the total value of tickets sold was $1,506. Student tickets sold for $6 each and adult tickets sold for $9 each. The number of adult tickets sold was five less than three times the number of student tickets sold. How many student tickets and how many adult tickets were sold?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
Step 1. Read the problem.
- Determine the types of tickets involved. There are student tickets and adult tickets.
- Create a table to organize the information.
Step 2. Identify what we are looking for.
- We are looking for the number of student and adult tickets.
Step 3. Name. Represent the number of each type of ticket using variables.

We know the number of adult tickets sold was five less than three times the number of student tickets sold.
- Let s be the number of student tickets.
- Then $3 s - 5$ is the number of adult tickets
Multiply the number times the value to get the total value of each type of ticket.

Step 4. Translate. Write the equation by adding the total values of each type of ticket.

$6 s + 9 (3 s - 5) = 1506$

Step 5. Solve the equation.

$\begin{matrix} 6 s + 27 s - 45 & = & 1506 \\ 33 s - 45 & = & 1506 \\ 33 s & = & 1551 \\ s & = & 47 student tickets \end{matrix}$

$\begin{matrix} 3 s - 5 \\ 3 (47) - 5 \end{matrix}$

136 adult tickets

Step 6. Check the answer.

There were 47 student tickets at $6 each and 136 adult tickets at $9 each. Is the total value $1,506? We find the total value of each type of ticket by multiplying the number of tickets times its value then add to get the total value of all the tickets sold.

$\begin{matrix} 47 \cdot 6 & = & 282 \\ 136 \cdot 9 & = & \underset{_____}{1,224} \\ 1,506 ✓ \end{matrix}$

Step 7. Answer the question. They sold 47 student tickets and 136 adult tickets.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

The first day of a water polo tournament the total value of tickets sold was $17,610. One-day passes sold for $20 and tournament passes sold for $30. The number of tournament passes sold was 37 more than the number of day passes sold. How many day passes and how many tournament passes were sold?

How did it go?

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solution

Your turn

Solution

Your turn