Algebra: Ticket Word Problems

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
  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.

 

 

Tickets word problem 

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?

 

 

 

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