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Assignment
Name:______________
SOLVING WORD PROBLEMS (using Systems)
Due Date: Thursday April 1 (no joke )
Present complete solutions to solve the following word problems using linear
systems. Each question is worth 5 marks. Communication (ie. Mathematical
form) will be marked.
Total Marks: 25
1.
Carlos has a jar of coins in which he places quarters and dimes. There are twice as many
quarters as dimes in the jar. The total amount in the jar is $48.
a) Let q represent the number of quarters and d represent the number of dimes. Write a
system of linear equations to represent the situation.
b) How many of each coin does Carlos have?
2.
The school council plans to have a barbecue lunch for the whole school to celebrate its
victory in the volleyball finals. They need a total of 400 hot dogs and hamburgers. Hot dogs
cost $0.25 each and hamburgers cost $0.80 each. They have a budget of $166 for the event.
a) Let x represent the number of hot dogs and y represent the number of hamburgers.
Write a system of linear equations to represent the situation.
b) How many of each does the school council buy?
3.
Tickets for a movie cost $13 for adults and $8 for children. A total of 400 tickets were sold
and total sales were $4650. How many of each type of ticket were sold?
4.
The school band is getting new uniforms. Stylus Company will make them at a cost of $200
for labour plus $12 per uniform for fabric. Trend Setters is charging $176 for labour plus $14
per uniform for fabric.
a) Let n represent the number of uniforms and C represent cost. For what number of
uniforms are the charges the same for the two companies?
b) Which company is more affordable if 20 band uniforms are needed?
Bonus Question: Create your own word problem that can be solved using a system of equations.
Include a complete solution with your problem.
1.
Answer Key
a) The situation can be represented by the linear system
Q = 2D
0.25Q + 0.10D = 48
b) Solve the system of equations. In this case, substitution is probably the simplest method.
Q = 2D 
0.25Q + 0.10D = 48

Substitute equation  into equation .
0.25Q + 0.10D = 48
0.25(2D) + 0.10D = 48
0.5D + 0.10D = 48
0.60D = 48
D = 80
Substitute this value for D into equation .
Q = 2D
Q = 2(80)
Q = 160
Carlos has 160 quarters and 80 dimes.
2.
+
a) The situation can be represented by the linear system
x + y = 400

0.25x + 0.8y = 166

b) Solve the system of equations. In this case, elimination is a good method of solving the system.
Multiply each term in equation  by 4.
Label the new equation  and subtract it from equation .
x+
y = 400

x + 3.2y = 664

–2.2y = –264
y = 120
Substitute the value for y into equation .
x + y = 400
x + 120 = 400
x + 120 – 120 = 400 – 120
x = 280
The school council needs to buy 280 hot dogs and 120 hamburgers.
3. Let x represent the number of adult tickets sold and y represent the number of children’s tickets sold.
The situation can be represented by the linear system
x + y = 400

13x + 8y = 4650

Multiply equation  by 8. Label the new equation  and subtract it from equation .
13x + 8y = 4650 
–
8x + 8y = 3200 
5x
= 1450
x = 290
Substitute this value of x into equation .
x + y = 400
290 + y = 400
290 + y – 290 = 400 – 290
y = 110
290 adult tickets and 110 children’s tickets were sold.
4. The situation can be represented by the linear system
C = 200 + 12n
C = 176 + 14n
where n is the number of uniforms.
Use substitution to solve the system for n.
200 + 12n = 176 + 14n
200 + 12n – 12n = 176 + 14n – 12n
200 = 176 + 2n
200 – 176 = 176 + 2n – 176
24 = 2n
12 = n
The charges for both companies will be the same if 12 uniforms are made.