Algebra: Ticket Word Problems

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

Related Topics:
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

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?



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

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

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

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?



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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