8.4 Word Problems
Math 9
The length of a rectangular garden is 1 m more than
three times the garden’s width. If the perimeter of the
garden is 34 m, find its dimensions.
The length of a rectangular garden is 1 m more than
three times the garden’s width. If the perimeter of the
garden is 34 m, find its dimensions.
3X + 1
X
X
3X + 1
Let x = the width of the rectangle
Let 3x + 1 = the length of the rectangle
Let x = the width of the rectangle
Let 3x + 1 = the length of the rectangle
34/2 = 3x + 1 + x
17 = 4x + 1
-1
-1
16 = 4x
3X + 1
÷4 ÷4
4=x
Length of rectangle: 3x + 1 = 3(4) + 1 = 13
The width of the rectangle is 4 and the length of the
rectangle is 13.
X
The cash register in the school canteen contains x
quarters and (30 – x) dimes. If the total value of the
coins is $5.85, how many of each kind of coin are
there?
The cash register in the school canteen contains x
quarters and (30 – x) dimes. If the total value of the
coins is $5.85, how many of each kind of coin are
there?
Multiply 0.10 into the brackets
0.25x + 0.10(30-x) = 5.85
0.25x + 3.00 - 0.10x = 5.85
0.15x + 3.00 = 5.85
- 3.00
-3.00
0.15x = 2.85
÷0.15 ÷0.15
x = 19
Combine x values
Get term with x by
itself
Isolate x
The cash register in the school canteen contains x
quarters and (30 – x) dimes. If the total value of the
coins is $5.85, how many of each kind of coin are
there?
0.25x + 0.10(30-x) = 5.85
Dimes = 30 – x
0.25x + 3.00 - 0.10x = 5.85
= 30 – 19 = 11
0.15x + 3.00 = 5.85
- 3.00
-3.00
0.15x = 2.85
÷0.15 ÷0.15
There are 11 dimes and 19
x = 19
quarters in the canteen
An employee mixes peanuts worth $2.80/kg with cashews worth
$3.60/kg. She sells the mixture for $3.12/kg. If she has 75 kg of
peanuts, how many kilograms of cashews does she need?
An employee mixes peanuts worth $2.80/kg with cashews worth
$3.60/kg. She sells the mixture for $3.12/kg. If she has 75 kg of
peanuts, how many kilograms of cashews does she need?
Let x = the amount of peanuts in the ratio
Let 1-x = the amount of cashews in the ratio
2.80x + 3.60(1-x) = 3.12
2.80x + 3.60 – 3.60x = 3.12
3.60 – 0.80x = 3.12
-3.60
-3.60
-0.80x = -0.48
÷-0.80 ÷-0.80
X = 0.6
1- x = 0.4
0.4
𝑥
=
0.6 75
75∗ 0.4 ÷ 0.6 = 50
75 kilograms of cashews are
needed to create this
mixture.
Time, Rate and Distance
2h x 100km/h = 200 km
2ℎ 100 𝑘𝑚
∗
= 200𝑘𝑚
1
1ℎ
What is the rate if you travel
150 km in 3 h?
150 𝑘𝑚 50 𝑘𝑚
=
𝑜𝑟 50 𝑘𝑚/ℎ
3ℎ
1ℎ
How long does it take to
travel 900 km at 75 km/h?
900 ÷ 75 = 12
900 𝑘𝑚
1ℎ
∗
= 12
1
75 𝑘𝑚
Plane A leaves the airport. One hour later, Plane B leaves the
same airport on the same course. It catches up to Plane A in 2 ½
h. The average speed of Plane B is 300 km/h faster than Plane A.
Find the speed of each plane.
Plane A leaves the airport. One hour later, Plane B leaves the
same airport on the same course. It catches up to Plane A in 2 ½
h. The average speed of Plane B is 300 km/h faster than Plane A.
Find the speed of each plane.
That means
Before you can
Plane A is
answer this
Let a = the speed of Plane A
travelling at
question you
Let 300 + a = the speed of Plane B
750km/h and
must ask your
Plane B is
self what will be
travelling at 1050
3.5a =2.5(300+a)
Its Distance, equal at the end
km/h.
which is
3.5a = 750 + 2.5a
calculated by
-2.5a
-2.5a
multiplying
a = 750
speed with time
300+ a = 300 +750 =1050
THAT’S IT FOR NOW