year 8 maths

1I
Applying algebra
43
13 Roberto draws a rectangle with unknown dimensions. He notes that the area is (x − 3)(y − 4) .
y − 4
x − 3
a If x = 5 and y = 7 , what is the area?
b What is the value of (x − 3)(y − 4) if x = 1 and y = 1 ?
c Roberto claims that this proves that if x = 1 and y = 1 then his rectangle has an area of 6 . What
is wrong with his claim?
(Hint: try to work out the rectangle’s perimeter.)
14 Tamir notes that whenever he hires an electrician, they charge a call-out fee $F and an hourly rate
of $H per hour.
a Write an expression for the cost of hiring an electrician for 1 hour.
b Write an expression for the cost of hiring an electrician for 2 hours.
c Write an expression for the cost of hiring an electrician for 30 minutes.
d How much does it cost to hire an electrician for t hours?
ENRICHMENT
– –
15
Ticket sales
15 At a carnival there are six different deals available to reward loyal customers.
Deal Entry cost ($) Cost per ride ($)
A 79 0
B 50 2
C 31 4
D 18 6
E 7 8
F 0 10
The queue consists of 100 customers. The first customer knows they will go on one ride, the
second will go on two rides, and the pattern continues, with the 100 th customer wanting to go on
100 rides. Assuming that each customer can work out their best deal, how many of each deal will
be sold?
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.