Ch 5.5
System Word Problems
Objective:
To set up linear equation word problems
and solve for the two unknown values.
Rules
1. Identify the two unknown values in the
problem and designate variables for them.
2. Set up Equation 1 using both variables
3. Set up Equation 2 using both variables
4. Line up like terms and solve the system
Example 1
The sum of two numbers is 19. Their difference is 1.
What are the numbers?
Let a = first number
Equation 1: sum
Let b = second number
a + b = 19
+
Equation 2: difference
a−b= 1
2a
2
= 20
2
a = 10
a−b= 1
10 − b = 1
b=9
Classwork
1) The sum of two numbers is 31. Their difference is 1.
What are the numbers ?
2) The difference of two numbers is 1. Their sum is 25.
What are the numbers ?
Example 2
Kim’s school is selling tickets to the school play. On the
first day of ticket sales the school sold 8 adult tickets and
7 child tickets for a total of $81. The school took in $130
on the second day by selling 8 adult tickets and 14 child
tickets. What was the price of each type of ticket?
Let a = adult ticket
Let c = child ticket
Equation 1: first day
Equation 2: second day
8a + 7c = 81
− 8a + 14c = 130
-7c = -49
-7
-7
c=7
8a + 7c = 81
8a + 7( 7 ) = 81
a=4
Example 3
Jill and Brenda are selling pies for a school fundraiser. Jill
sold 12 blueberry pies and 4 apple pies for a total of $184.
Brenda sold 3 blueberry pies and 4 apple pies for a total of
$103. Find the cost of each of the pies.
Let b = blueberry pie
Equation 1: Jill
Equation 2: Brenda
Let a = apple pie
12b + 4a = 184
− 3b + 4a = 103
9b
9
= 81
9
b=9
3b + 4a = 103
3(9 )+ 4a = 103
a = 19
Example 4
Daniel and James are selling fruit for a school fundraiser.
Customers can buy small boxes and large boxes of
tangerines. Daniel sold 10 small boxes and 3 large boxes
for a total of $169. James sold 8 small boxes and 12 large
boxes for a total of $260. What is the cost for each size
box of tangerines?
Let s = small box
Let L = large box
Equation 1: Daniel -4(10s + 3L = 169)
Equation 2: James
8s + 12L = 260
+
-40s − 12L = -676
-32s
= -416
-32
-32
s = 13
10s + 3L = 169
10(13)+ 3L = 169
L = 13
Classwork
3) Julio and Perry each improved their yards by planting rose
bushes and ivy. They bought their supplies from the same
store. Julio spent $219 on 9 rose bushes and 13 pots of
ivy. Perry spent $135 on 9 rose bushes and 6 pots of ivy.
What is the cost for each of the shrubbery plants?
4) Shreya and Eugene are selling wrapping paper for a
school fundraiser. Shreya sold 9 rolls of plain wrapping
paper and 8 rolls of holiday wrapping paper for a total of
$234. Eugene sold 12 rolls of plain wrapping paper and 6
rolls of holiday wrapping paper for a total of $228. What
is the cost of each type of wrapping paper?
5) The school that Joe goes to is selling tickets to a play. On
the first day of ticket sales the school sold 11 senior
citizen tickets and 4 student tickets for a total of $171.
The school took in $109 on the second day by selling 3
senior citizen tickets and 10 student tickets. What is the
price of each ticket?
6) Jenny’s school is selling tickets to the annual dance
competition. On the first day of ticket sales the school
sold 9 adult tickets and 6 student tickets for a total of
$204. The school took in $164 on the second day by
selling 8 adult tickets and 4 student tickets. What is the
price of each type of ticket?