Name of Lecturer: Mr. J.Agius
Course: HVAC1
Lesson 11
Chapter 3: Ratios & Proportion

Building ratios from story sums
Example 1
A family has 12 pets of which 6 are cats or kittens, 2 are dogs and the rest are birds. Find the
ratio of the numbers of
a) birds to dogs
b) birds to pets.
Answer
There are 4 birds
a) Number of birds : number of dogs
=4:2
=2:1
b) Number of birds : number of pets
= 4 : 12
=1:3
Example 2
Leaf green paint is made by mixing yellow and blue. Three tins of
yellow are mixed with one tin of blue to make a green colour.
Write down this in ratio form.
Answer
Yellow
3
3 Ratios & Proportion
:
:
Blue
1
=
=
Green
4
Page 1
Name of Lecturer: Mr. J.Agius

Course: HVAC1
Finding Missing Quantities
We know that ratios can be expressed as fractions. We also know that two ratios are equal
because the corresponding fractions are equal. So, in order to find a missing quantity, that is not
so obviously to note, we first express it as a fraction and then find the missing number as we
used to do.
Example 3
Find the missing numbers in a)
6:5=
: 10
b)
:4=3:5
Answer
(Fill the gap with an x to start with.)
a)
6 : 5 = x : 10
b)
x:4=3:5
i.e.
6 : 5 = 12 : 10
Write as fraction
x
3
=
4
5
Make x as subject of the formula
x=4
So
2
3
2
=2
5
5
2
:4=3:5
5
Example 4
Two speeds are in the ratio 12 : 5. If the first speed is 8 km/h, what is the second speed?
Answer
Let the second speed be x km/h. Then 8 : x = 12 : 5
We can also write this ratio as
x : 8 = 5 : 12
Note that 8 is still associated to 12 and x to 5. So this step is correct.
Write as fraction
Make x subject of the formula
x 5

8 12
8  5 10
1
x

3
12
3
3
1
So, the second speed is 3 km/h
3
3 Ratios & Proportion
Page 2
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Building Ratios from Story Sums
In each question give your answer in its simplest form.
Q1
Two brothers have €20 and €24 in their respective savings accounts.
Express these amounts as a ratio
Q2
Miss Morgan has €320 in her current account, €400 in her deposit account, and €800 in her
savings account.
Express these amounts as a ratio.
Q3
The sides of a triangle are ¾, ½ and ¼. Writes these sides as a ratio in its simplest form.
Q4
Two angles of a triangle are 54 and 72. Find the ratio of the size of the third angle to the sum
of the first two.
Q5
A man earns €5500 and pays income tax of €860. What is the ratio of tax to earnings?
Q6
A snack bar sells 84 cans of cola and 54 cans of lemonade. Write down and simplify the ratio of
the sales of cola to lemonade.
Q7
There are 280 vehicles in a car park; 42 are vans and the rest are cars. Find the ratio of the
number of cars to the number of vans.
Q8
Find
a) the cost of 11m2 of vinyl flooring at €8.40 per square metre
b) the cost of 44 vinyl tiles at €2.40 each
c) the ratio of the cost of the vinyl flooring to the cost of the tiles.
Q9
The diagram shows the design of a garden.
3m
Patio
2m
1.5m
Pond
2m
2m
Flower bed
4m
8m
Find the ratio of the areas of: (take   3)
a) the patio to the lawn
b) the pond to the patio
c) the flower bed to the lawn.
3 Ratios & Proportion
Page 3
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Finding Missing Quantities
Exercise 1
Find x in the following ratios.
a)
d)
2:5=4:x
10 : 3 = x : 5
b)
e)
9:6=x:4
7 : 24 = x : 960
c)
f)
3:x=2:5
x : 15 = 12 : 120
Exercise 2
Q1
The ratio of the amount of money in David’s pocket to that in Indira’s pocket is 9 : 10. Indira
has 25c. How much has David got?
Q2
A class is making a model of the school building and the ratio of the lengths of the model to the
lengths of the actual building is 1 : 20. The gym is 6 m high. How high, in centimetres, should
the model of the gym be?
Q3
Spring bulbs are planted in a border in the ratio of 3 yellow tulips to 2 pink tulips to 5 grape
hyacinths.
If 615 yellow tulip bulbs are planted, how many pink tulip bulbs and how many grape hyacinth
bulbs are planted?
Q4
Two terracotta pots have volumes in the ratio of 2 : 9. The smaller can hold 3kg of peat. What
weight of peat can the larger pot hold?
Q5
In a rectangle, the ratio of length to width is 9 : 4. The length is 24 cm. Find the width.
Q6
To mix plant food, one mixes 20ml of plant food with one litre of water.
a)
How much of this plant food would you mix with 3 litres of water?
b)
What is the correct mixing ratio of plant food to water? Write this ratio in its simplest
form.
Q7
The distance ‘as the crow flies’ between Apton and Bendale is 12km. The scale of a map of this
area is 1 : 250 000. What is the distance between Apton and Bendale on the map?
3 Ratios & Proportion
Page 4