Loading…
Example 3.30 from Elementary Algebra, 3.3 Solve Mixture Applications
Solve Mixture Applications: example 3.30
Galen sold 810 tickets for his church’s carnival for a total of $2,820. Children’s tickets cost $3 each and adult tickets cost $5 each. How many children’s tickets and how many adult tickets did he sell?
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.
Solution
Step 1. Read the problem.
- Determine the types of tickets involved. There are children 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 children and adult tickets.
Step 3. Name. Represent the number of each type of ticket using variables.
- We know the total number of tickets sold was 810. This means the number of children’s tickets plus the number of adult tickets must add up to 810.
- Let c be the number of children tickets.
- Then 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.
Step 5. Solve the equation.
How many adults?
Step 6. Check the answer. There were 615 children’s tickets at $3 each and 195 adult tickets at $5 each. Is the total value $2,820?
Step 7. Answer the question. Galen sold 615 children’s tickets and 195 adult tickets.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
During her shift at the museum ticket booth, Leah sold 115 tickets for a total of $1,163. Adult tickets cost $12 and student tickets cost $5. How many adult tickets and how many student tickets did Leah sell?
How did it go?