Ch 5.5System 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 Let b = second number

Equation 1: a + b = 19

Equation 2: a − b = 1+

2 22a = 20

a = 10

a − b = 1− b = 110

b = 9

sum

difference

1)

Classwork

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: 8a + 7c = 81

Equation 2: 8a + 14c = 130−

-7 -7-7c = -49

c = 7

first day

second day

8a + 7c = 818a + 7( ) = 817

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 Let a = apple pie

Equation 1: 12b + 4a = 184

Equation 2: 3b + 4a = 103−

9 99b = 81

b = 9

Jill

Brenda 3b + 4a = 1033( )+ 4a = 1039

a = 19

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?

Example 4

Let s = small box Let L = large box

Equation 1: 10s + 3L = 169

Equation 2: 8s + 12L = 260+

-32 -32-32s = -416

s = 13

10s + 3L = 16910( )+ 3L = 16913

L = 13

Daniel

James

-4( )

-40s − 12L = -676

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?

3)Classwork

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?

4)

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?

5)

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?

6)