Ticket difficulties are native problems comparable to coin problems and also stamp problems as tickets might be denominated in specific values.

You are watching: The number of tickets sold for a concert during each hour

Be mindful to distinguish between the value of the items and also the quantity of the items.

A table have the right to be useful for distinguishing in between quantity and value in this kind of indigenous problems.

**Example:**The expense of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets to be sold and $950 to be collected. How countless tickets the each form were sold?

**Solution:**Step 1: collection up a table through quantity and value.

$3 tickets | |||

$2 tickets | |||

together |

Step 2: fill in the table with details from the question.

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The expense of tickets because that a pat is $3.00 because that adults and $2.00 for children. 350 tickets were sold and also $950 was collected. How numerous tickets the each form were sold?

Let x = number of $3 ticketsLet y = number of $2 ticketsTotal = quantity × value

quantity value complete$3 tickets | x | 3 | 3x |

$2 tickets | y | 2 | 2y |

together | 350 | 950 |

Step 3: include down each obelisk to get the equations

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

Use Substitution MethodIsolate variable x in equation 1

x = 350 – y (equation 3)

Substitute equation 3 right into equation 2

3(350 – y) + 2y = 9501050 – 3y + 2y = 9503y – 2y = 1050 – 950y = 100

Substitute y = 100 right into equation 1

x + 100 = 350x = 250

Answer: 250 $3 tickets and 100 $2 tickets to be sold.

### Ticket indigenous Problems

**Example:**Jim offered 120 ticket to a game. Adult tickets room $24 each and children tickets space $13 each. Sales are $2110. How numerous of each was sold?

**Example:** 500 world see a play. Children are fee $15 and also adults $25. Ticket proceeds room $11,250. Exactly how many children attended the play?

**Example:** for a theater showing 202 tickets were sold. A child’s ticket expenses $6.00 and also an adult’s ticket costs $10.00. How plenty of tickets of every were marketed if the receipts totaled $1708.00?

**Example:** The Goonies sold 785 concert tickets for a full of $17,650. If great tickets cost $40 and cheap tickets expense $15, how numerous of each form of ticket did they sell?

**Example:** in ~ the arcade, Sammy won two blue tickets, 1 yellow ticket and also 3 red tickets for a complete of 1,500 points. Jamal won 1 blue, 2 yellow and also 2 red because that 1225 points. Yvonne winner 2 blue, 3 yellow and 1 red because that 1200 points. How much is every ticket worth?

**Example:** For opened night 328 tickets were sold. Students payment $2 every while non-students payment $4 each. If a total of $910 were collected, how countless students and also how numerous non-students attended?

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