year 8 maths

2D
Equations with pronumerals on both sides
81
PROBLEM-SOLVING AND REASONING
8, 12 8–10, 12, 13
9–11, 13, 14
8 Write an equation and solve it systematically to find the unknown number in these problems.
a Doubling x and adding 3 is the same as tripling x and adding 1 .
b If z is increased by 9 , this is the same as doubling the value of z .
c The product of 7 and y is the same as the sum of y and 12 .
d When a number is increased by 10 , this has the same effect as tripling the number and
subtracting 6 .
9 Find the value of x and y in the following rectangles.
a
3x + 2
y + 3 3y − 17
5x − 10
b
3y − 18
2x x + 4
y − 4
10 Find the area and the perimeter of this rectangle.
8x − 21
2y − 4 y + 8
4x + 7
11 At a newsagency, Preeta bought four pens and a $1.50 newspaper, while her husband Levy bought
two pens and a $4.90 magazine. To their surprise the cost was the same.
a Write an equation to describe this, using p for the cost of a single pen.
b Solve the equation to find the cost of a pen.
c If Fred has a $20 note, what is the maximum number of pens that he can purchase?
12 To solve the equation 12 + 3x = 5x + 2 you can first subtract 3x or subtract 5x .
a Solve the equation above by first subtracting 3x .
b Solve the equation above by first subtracting 5x .
c What is the difference between the two methods?
13 Prove that the rectangular shape shown must be a square. (Hint: first find the values of x and y .)
3x + 5
6y − 7 5y − 1
2x + 13
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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