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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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