Translating Words Into Symbols

Part A: Translate each of the following expression with a mathematical symbol.

1. Altogether _____

2. Sum _____

3. Increase _____

4. Difference _____

5. Decrease _____

6. Product _____

7. Quotient _____

8. Is _____

+++-

-×÷=

Part B: For the following statements, define two variables and write a linear equation that models the sentence.

1. The sum of two numbers is 7. _________

2. The sum of the width and length of a rectangle is 36 m.

_________

3. The total value of nickels and dimes is 75 cents.

_________

x + y = 7

l + w = 36

5n + 10d = 75

4. The cost of the rental is $50 plus $5/h.

___________

5. A rectangle is 2 m longer than it is wide.

___________ 6. When 3 times the first number is subtracted from the second number, the result is 20.

___________

C = 5h + 50

L = w + 2

s – 3f = 20

7. Mary has x $5 bills and y $10 bills.

a) The total value of bills in dollars.

_______________

b) The total number of bills.

_______________

T = 5x + 10y

N = x + y

8. Aaron has x dimes and y quarters.

a) The value of dimes in cents. _________

b) The value of quarters in dollars. _________

c) The total value of coins in cents.

__________________

10x

T = 10x + 25y

0.25y

d) The total number of coins.

__________________ N = x + y

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 + 0.09y = 88

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

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 + 2550

Revenue: M = 25p

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 + 0.05n = 20

d + n = 300

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 + 0.15c = 0.06(20)0.03m + 0.15c = 1.2

Speed/Distance/Time Relationship

speed distance

time sd

t

distance speed time

timedistance

speed

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

c + t = 1.5 60c + 90t = 95

Speed Time Distance

By Car

By Train

Total

60

90

c

t

60c90t

1.5 95

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 riverRecall: (speed)(time) = distance(c + r)(2) = 12______ ___ 2 2

c + r = 6

(c – r)(3) = 12______ ___ 3 3

c – r = 4