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1
Translate the following situations using a system of equations. Use the variables x and y.
a)
Saturday at the cinema, Paul counts 312 people. Lisa finds that there are two times more children than
adults. Determine how many children and adults there are at the cinema.
b)
The sum of two numbers is 54 and their difference is 30. What are the numbers?
c)
Half of the sum of two numbers is 40 and half of their difference is 24. What are the numbers?
d)
Six records and four cassettes cost $116.00, whereas eleven records and four cassettes cost $183.00.
Find the cost of a cassette.
e)
The difference between two numbers is 5 and the quotient of the larger number by the smaller is 5.
What are the numbers?
2
Solve the systems you created in Question 1.
3
Solve the following systems using the substitution method.
a)
3x  y = 2
b)
c)
x  y 5
y =  x  10
4
2 x  y  1
x  y  2
2x  3y  9
Solve the following systems using the elimination method.
a)
2x  y  7
4x  2 y  2
b)
12 x  5 y  27
3x  5 y  15
c)
12 x  7 y  20
5x  3 y  11
5
A woman bought $33.00 worth of bus tickets. Adult bus tickets cost $2.50 each and children's bus tickets cost
$1.00 each. She bought 4 times more adult tickets than children's tickets. How many tickets of each type did
she buy?
6
A vending machine sells apples for $0.40 and oranges for $0.45. At the end of the day the owner finds that 90
fruits were sold for a total of $38.00. How many apples and how many oranges were sold?
7
To belong to a tennis club, a member must pay an amount (y) to register in the club. It then costs an additional
amount (x) for each hour of tennis. Anne and Julie have now been members for a few months. So far, Anne has
spent $327 for 21 hours of tennis and Julie has spent $264 for 12 hours of tennis. How many hours will Julie
have to play tennis in order for her to spend $845?
8
A restaurant has only tables for 4 people and tables for 6. There are 100 places in all. There are 5 more tables
for 4 than tables for 6. Find the number of tables for 4 and the number of tables for 6.