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.
Ticket Word Problems
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
Word Problems With Theater Attendance
Example:
500 people see a play. Children are charged $15 and adults $25. Ticket proceeds are $11,250. How many children attended the play
Algebra - Word Problems: With Movie Tickets
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