Ticket problems are algebra word problems that involve various tickets of different values.

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

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

Let 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.

**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?

**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?

**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?

**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:**

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?

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