# Algebra: Ticket Word Problems

Ticket problems are word problems similar to coin problems and stamp problems as tickets may be denominated in specific values.

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More Algebra Word Problems and Algebra Help

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Be careful to distinguish between the value of the items and the quantity of the items.
A table can be useful for distinguishing between quantity and value in this type of word problems.

Example:

The cost of tickets for a play is \$3.00 for adults and \$2.00 for children. 350 tickets were sold and \$950 was collected. How many tickets of each type were sold?

Solution:

Step 1: Set up a table with quantity and value.

 quantity value total \$3 tickets \$2 tickets together

Step 2: Fill in the table with information from the question.

The cost of tickets for a play is \$3.00 for adults and \$2.00 for children. 350 tickets were sold and \$950 was collected. How many tickets of each type were sold?

 Let x = number of \$3 tickets y = number of \$2 tickets Total = quantity × value

 quantity value total \$3 tickets x 3 3x \$2 tickets y 2 2y together 350 950

Step 3: Add down each column to get the equations

x + y = 350                    (equation 1)
3x + 2y = 950                 (equation 2)

Use Substitution Method
Isolate variable x in equation 1

x = 350 – y                     (equation 3)

Substitute equation 3 into equation 2

3(350 – y) + 2y = 950
1050 – 3y + 2y = 950
3y – 2y = 1050 – 950
y = 100

Substitute y = 100 into equation 1

x + 100 = 350
x = 250

Answer: 250 \$3 tickets and 100 \$2 tickets were sold.

### Ticket Word Problems

Example: Jim sold 120 tickets to a game. Adult tickets are \$24 each and children tickets are \$13 each. Sales are \$2110. How many of each was sold?
Example: 500 people see a play. Children are charged \$15 and adults \$25. Ticket proceeds are \$11,250. How many children attended the play?

Algebra - Word Problems: With Movie Tickets

Example: For a theater showing 202 tickets were sold. A child's ticket costs \$6.00 and an adult's ticket costs \$10.00. How many tickets of each were sold if the receipts totaled \$1708.00?
Word problem - mixture of ticket sales

Example: For opening night 328 tickets were sold. Students paid \$2 each while non-students paid \$4 each. If a total of \$910 were collected, how many students and how many non-students attended?

Solve word problems in three variables

Example: At the arcade, Sammy won two blue tickets, 1 yellow ticket and 3 red tickets for a total of 1,500 points. Jamal won 1 blue, 2 yellow and 2 red for 1225 points. Yvonne won 2 blue, 3 yellow and 1 red for 1200 points. How much is each ticket worth?
Example: The Goonies sold 785 concert tickets for a total of \$17,650. If good tickets cost \$40 and cheap tickets cost \$15, how many of each type of ticket did they sell?

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