year 8 maths

86 Chapter 2 Equations 2
12 Kate’s age 5 years ago, when doubled, is equal to triple her age 10 years ago.
a Write an equation to describe this, using k for Kate’s current age.
b Solve the equation to find Kate’s current age.
13 Rectangles A and B have the same area.
6
5
10 A
x
B
15.5
a What is the value of x ?
b State the perimeter of the shape shown above.
14 Abraham is asked how many people are in the room next door. He answers that if three more
people walk in and then the room’s population is doubled, this will have the same effect
as quadrupling the population and then 11 people leaving. Prove that what Abraham said
cannot be true.
15 Ajith claims that three times his age 5 years ago is the same as nine times how old he will be
next year. Prove that what Ajith is saying cannot be true.
16 A common mistake when expanding is to write 2(n + 3) as 2n + 3 . These are not equivalent,
since, for example, 2(5 + 3) = 16 and 2 × 5 + 3 = 13 .
a Prove that they are never equal by trying to solve 2(n + 3) = 2n + 3 .
b Prove that 4(2x + 3) is never equal to 8x + 3 but it is sometimes equal to 4x + 12 .
ENRICHMENT
– –
17
Challenging expansions
17 Solve the following equations. Note that, in general, your answers will not be integers.
a 2(3x + 4) + 5(6x + 7) = 64x + 1
b −5(3p + 2) + 5(2p + 3) = −31
c −10(n + 1) + 20(2n + 13) = 7
d 4(2q + 1) − 5(3q + 1) = 11q − 1
e x + 2(x + 1) + 3(x + 2) = 11x
f m − 2(m + 1) − 3(m − 1) = 2(1 − 4m)
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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