© John Wiley & Sons Australia, Ltd 2012 Page 1

WorkSHEET 8.1 Direct proportion Name: ___________________________ 1 Given the table below, where 𝑦 is directly

proportional to 𝑥, complete the table to find the constant of proportionality, 𝑘, and write the rule connecting the two variables:

x 2 5 6 y 12

15

30

x 2 4 5 6 10 y 6 12

15

18 30

𝑘 = 3

𝑦 = 3𝑥

2 When travelling at constant speed, Kylie’s car can travel 240 kilometres in 3 hours. Here we can say that the distance travelled is directly proportional to the time taken. (a) Find the constant of proportionality (b) Hence, state the rule relating distance (d)

to time (t). (c) Use your rule to predict the time it would

take to cover 880 kilometres.

(a)

𝐷 ∝ 𝑡 𝐷 = 𝑘𝑡

when 𝑡 = 3, then 𝐷 = 240 240 = 𝑘 × 3 𝑘 = 80

(b)

𝐷 = 80𝑡 (c)

880 = 80𝑡

𝑡 =88080

𝑡 = 11

It would take 11 hours to travel 880km

© John Wiley & Sons Australia, Ltd 2012 Page 2

3 If u µ v and when u = 18, v = 48, find k, the constant of proportionality.

u µ v

4 If y is directly proportional to x and the constant of proportionality is 4, when the value of x is 20, what is the value of y?

Solution: 𝑦 ∝ 𝑥 𝑦 = 𝑘𝑥

𝑦 = 4 × 20 𝑦 = 80

5 If a vehicle uses 6 litres of fuel for every 100 km and the amount of fuel used is directly proportional to the distance travelled, how much fuel do you need to travel 475km?

Given, 𝐹 ∝ 𝑑

so 𝐹 = 𝑘𝑑

When F=6, d=100 6 = 𝑘 × 100

𝑘 =6100

𝑘 =350

Therefore;

𝐹 =350𝑑

Now set d=475

𝐹 =350 × 475 = 28.5

So you will need 28.5 litres to travel 475 km.

8348184818

=

=

´==

k

kkvu

© John Wiley & Sons Australia, Ltd 2012 Page 3

6 The cost of producing copper wire is directly proportional to the length. If it costs $5 for a 60-m length, find the constant of proportionality.

Let l = length of wire and Let c = cost of producing wire c µ l

7 If a vehicle uses 7 litres of fuel for every 100 km and the amount of fuel used is directly proportional to the distance travelled, how far can you travel on 37 litres of fuel?

Given, 𝐹 ∝ 𝑑

so 𝐹 = 𝑘𝑑

When F=7, d=100 7 = 𝑘 × 100

𝑘 =7100

Therefore;

𝐹 =7100𝑑

Now set F=37

37 =7100 × 𝑑

𝑑 =37 × 100

7

= 528.57 So you will can travel 528 km on 37 litres.

121605605

=

=

´==

k

kklc

© John Wiley & Sons Australia, Ltd 2012 Page 4

8 The time taken to ride the length of a cycling course is directly proportional to the length of the course. If it took 3 hours to cycle a 140-kilometre course, how long will it take to cycle a 180-kilometre course?

Let l = length of course and Let t = time taken t µ l

9 A school has a boy to girl ratio of 6:7. If there are 270 boys, how many girls are there?

𝐵𝑜𝑦𝑠 ∶ 𝐺𝑖𝑟𝑙𝑠

6: 7 = 270: 𝑥

76 =

𝑥270

𝑥 = 315

10 The cost of producing a paperback novel is directly proportional to the number of pages. If it costs $3 to produce a book with 400 pages, how much will it cost to produce a book with 720 pages?

Let n = number of pages and Let c = cost c µ n

It will cost $5.40 to produce a book with 720 pages.

3 14031403140

When 1803 18014063 hours73 hours 51minutes

t klk

k

t l

l

t

== ´

=

=

=

= ´

=

=

3 40034003400

When 7203 720400275$5.40

c knk

k

c n

n

c

== ´

=

=

=

= ´

=

=