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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