Ticket problems are word problems similar to coin problems and stamp problems as tickets may be denominated in specific values.
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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 1x = 350 – y (equation 3)
Substitute equation 3 into equation 2
3(350 – y) + 2y = 950
1050 – 3y + 2y = 950
3y – 2y = 1050 – 950
y = 100Substitute y = 100 into equation 1
x + 100 = 350
x = 250
Answer: 250 $3 tickets and 100 $2 tickets were sold.