1. Translating Words Into Symbols
Part A: Translate each of the following expression with a mathematical symbol. + -
1. Altogether _____
5. Decrease _____ + ×
2. Sum _____
6. Product _____ + ÷
3. Increase _____
7. Quotient _____ - =
4. Difference _____
8. Is _____

2. Part B: For the following statements, define two variables and write a linear equation that models the sentence.
x + y = 7
1. The sum of two numbers is _________
2. The sum of the width and length of a rectangle is 36 m.
_________
l + w = 36
3. The total value of nickels and dimes is 75 cents.
_________
5n + 10d = 75

3. 4. The cost of the rental is $50 plus $5/h.
___________
C = 5h + 50
5. A rectangle is 2 m longer than it is wide ___________
L = w + 2
6. When 3 times the first number is subtracted from the second number, the result is 20.
___________
s – 3f = 20

4. T = 5x + 10y N = x + y 7. Mary has x $5 bills and y $10 bills.
a) The total value of bills in dollars _______________
T = 5x + 10y
b) The total number of bills.
_______________
N = x + y

5. 10x 0.25y T = 10x + 25y N = x + y 8. Aaron has x dimes and y quarters.
The value of dimes in cents. _________
The value of quarters in dollars. _________
10x
0.25y
c) The total value of coins in cents.
__________________
T = 10x + 25y
d) The total number of coins.
__________________
N = x + y

6. Modelling with Linear Equations
 Model each situation using a linear system. Define two variables and write the equations.
1. Anne deposited $1200 in her bank accounts. How much did she put into her savings account, which pays 9% per year in interest, and her chequing account, which pays 4% per year, if she earned $88 in interest after one year?
Let x rep. the amount ($) in Anne’s chequing account
y rep. the amount ($) in Anne’s savings account
x + y = 1200
0.04x y = 88

7. 2. Art’s Car Rental charges $45 to rent a compact car for the day plus an additional $0.18/km. Budget Rentals charges $55/day and $0.10/km. How many kilometres would result in the same charge from both companies?
Let d rep. the distance travelled (km) in one day
C rep. the amount ($) charged each day
Art’s Car Rental: C = 0.18d + 45
Budget Rentals: C = 0.10d + 55

8. 3. Sara has started her own home business selling perfume on-line
3. Sara has started her own home business selling perfume on-line. Her start-up costs were $2550 for a new computer. She buys the perfume from her supplier for $15 per bottle and sells it for $25 per bottle. Determine the number of bottles she must sell to break even.
Let p rep. the number of perfume bottles
M rep. the amount of money
Expenses: M = 15p
Revenue: M = 25p

9. 4. Frank has $20 to purchase nickels and dimes from the bank for change for a craft fair. The bank teller gives Frank 300 coins in total. How many nickels and dimes were there?
Let d rep. the number of dimes
n rep. the number of nickels
0.1d n = 20
d + n = 300

10. 5. Milk and cream contain different percents of butterfat
5. Milk and cream contain different percents of butterfat. How much 3% milk needs to be mixed with how much 15% cream to give 20 L of 6% cream.
Let m rep. the amount (L) of 3% milk
c rep. the amount (L) of 15% cream
m + c = 20
0.03m c = 0.06(20)
0.03m c = 1.2

11. Speed/Distance/Time Relationship

12. 6. Jose travelled the 95 km from Oakville to Oshawa by car and GO train. The car averaged 60 km/h, and the train averaged 90 km/h. The whole trip took 1.5 h. How long was he in the car?
Let c rep. the time (hr) travelled by car
t rep. the time (hr) travelled by train
Speed
Time
Distance
By Car
By Train
Total 60 c
60c 90 t
90t
1.5 95
c + t = 1.5
60c + 90t = 95

13. 7. A canoeist took 2 hours to travel 12 km down a river
7. A canoeist took 2 hours to travel 12 km down a river. The return trip against the current took 3 hours. What was the average paddling rate of the canoeist? What was the speed of the current?
Let c rep. the speed (km/h) of the canoeist
r rep. the speed (km/h) of the river
Recall: (speed)(time) = distance
(c + r)(2) = 12
(c – r)(3) = 12
______ ___
______ ___
c + r = 6
c – r = 4