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Systems of Linear Equations Word Problems:

Solve the word problem:

1) Write a key for the word problem.

2) Gather information from the word problem (close reading, highlight, underline important information)

3) Write an equation from steps 1 and 2

4) Solve the equation

Brenda’s school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of each type of ticket?

A) Key : Let S = price of senior tickets

Let C = price of child tickets

B) Gather information: 3 senior citizen tickets sold &

9 child tickets sold for a of total $75; 8 senior tickets

& 5 child tickets sold for a total of $67.

C) Equation: 3s + 9c = 75

8s + 5c = 67

D) Solve: Substitution or Elimination method

Substitution: 3s + 9c = 75 and 8s + 5c = 67

1) Isolate S: 3s + 9c = 75; 3s + 9c – 9c = -9c+ 75 ;

3s = -9c + 75; 3s/3 = -9c/3 + 75/3 ;

S = -3c + 25

2) Substitute: S = -3c + 25 into 8s + 5c = 67;

8(-3c + 25) + 5c = 67

3) Execute: 8(-3c + 25) + 5c = 67; -24c + 200 + 5c=67

-19c + 200 = 67

-19c +200 – 200 = 67-200

-19c = -133

-19c/-19 = -133/-19

C = 7

4) Substitute: c = 7 into 3s +9c = 75

3s + 9(7) = 75

3s + 63 = 75

3s + 63 – 63 = 75 – 63

3s = 12

3s/3 = 12/3

S = 4

5) Solutions: Child Tickets cost $7 and Senior Tickets

Cost $ 4.

OR Use Elimination Method:

Steps: A and B are similar to above examples.

C) Equation: 3s + 9c = 75

8s + 5c = 67

Decide which variable you want to eliminate

By the LCM : Make 3 and 8 a 24 but make sure

Both are opposite integers.

8(3s + 9c = 75) and -3(8s + 5c = 67)

24s + 72c = 600 and -24s - 15c = 201

Then, combine like terms: 24s + 72c = 600

-24s -15c = -201

57c = 399

Solve: 57c = 399; 57c/57 = 399/57; c = 7

Substitute: c = 7 into one of the original equations

3s + 9c = 75; 3s + 9(7) = 75; 3s + 63 = 75

3s + 63- 63 = 75 – 63; 3s = 12; s = 4

Solutions: S = 4 and C = 7; Senior Tickets cost $4 &

Child Tickets cost $7.

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