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 is useful for distinguishing between quantity and value in this type of word problems.

Example 1:

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.

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