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Example 5.45 from Elementary Algebra, 5.5 Solve Mixture Applications with Systems of Equations
Solve Mixture Applications with Systems of Equations: example 5.45
Translate to a system of equations and solve:
The box office at a movie theater sold 147 tickets for the evening show, and receipts totaled $1,302. How many $11 adult and how many $8 child 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.
Solution
Step 1. Read the problem. We will create a table to organize the information. Step 2. Identify what we are looking for. We are looking for the number of adult tickets
and the number of child tickets sold.Step 3. Name what we are looking for. Let the number of adult tickets.
the number of child ticketsA table will help us organize the data.
We have two types of tickets: adult and child.Write a and c for the number of tickets. Write the total number of tickets sold at the
bottom of the Number column.Altogether 147 were sold. Write the value of each type of ticket in the
Value column.The value of each adult ticket is $11.
The value of each child tickets is $8.The number times the value gives the total
value, so the total value of adult tickets is
, and the total value of child
tickets isAltogether the total value of the tickets was
$1,302.Fill in the Total Value column. Step 4. Translate into a system of equations. The Number column and the Total Value
column give us the system of equations.
We will use the elimination method to solve
this system.Multiply the first equation by −8. Simplify and add, then solve for a. Substitute a = 42 into the first equation,
then solve for c.Step 5. Check the answer in the problem.
42 adult tickets at $11 per ticket makes $462
105 child tickets at $8 per ticket makes $840.
The total receipts are $1,302.✓Step 6. Answer the question. The movie theater sold 42 adult tickets and 105 child tickets.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Translate to a system of equations and solve:
The ticket office at the zoo sold 553 tickets one day. The receipts totaled $3,936. How many $9 adult tickets and how many $6 child tickets were sold?
How did it go?