Transcript 1. Modelling Linear Equations

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
4. Difference
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.
x_________
+y=7
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
_________
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
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
_______________
8. Aaron has x dimes and y quarters.
a) The value of dimes in cents.
_________
10x
0.25y
b) The value of quarters in dollars. _________
c) The total value of coins in cents.
T = 10x + 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
distance
speed 
time
distance  speed time
distance
time 
speed
d
s t
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
By Car
By Train
c + t = 1.5
Speed
60
Time
c
90
t
1.5
Total
Distanc
e
60c
90t
95
60c + 90t = 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 river
Recall: (speed)(time) = distance
(c
+
r)(2)
=
______ ___
12 2
2
c+r=6
(c – r)(3) =
______ ___
12
3
3
c–r=4