Pack B — Fluency

Mathematics

Year 8 · 8.8 Equations

Pack B · Fluency

Name: _________________________________

Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10

1.
Solve $7x = 56$ .
2.
Solve $x + -3 = 12$ .
3.
Solve $x - 12 = -3$ .
4.
Solve $\dfrac{x}{{a}} = 5$ .
5.
A function machine: $x \to \times 3 \to + 4 \to$ output. If output is 19, find $x$ .
6.
Solve $4x + -3 = 13$ .
7.
Solve $25 - x = 8$ .
8.
Check whether $x = 5$ is a solution to $2x + 3 = 13$ .
9.
Solve $-x = -8$ .
10.
Solve $-3x = 12$ where $rhs$ may be negative.

SilverQuestions 11–20

11.
Solve $5x + -4 = 21$ .
12.
Solve $4(x + -5) = 28$ .
13.
Solve $7x - 3 = 3x + 17$ .
14.
Solve $\dfrac{x}{{a}} + -1 = 4$ .
15.
Solve $7(x - 2) = 21$ .
16.
Solve $\dfrac{{a}x + -1}{{c}} = 5$ .
17.
A kite has two pairs of sides $(2n + 1)$ cm and $(3n - 2)$ cm. The perimeter is 28 cm. Find $n$ .
18.
Solve $5x + 12 = -3$ when $c$ is negative.
19.
I think of a number. I multiply by 4 and add 6. The result is 30. What is my number?
20.
A rectangle has length $(x + 5)$ and width $(x - 1)$ . Its perimeter is 28 cm. Find $x$ .

GoldQuestions 21–30

21.
Solve $\dfrac{{a}x - 2}{{c}} = 11$ .
22.
Solve $5(x - 2) = 3(6 + x)$ .
23.
Solve $\dfrac{x}{{a}} - \dfrac{x}{{b}} = 2$ .
24.
Pete has 3 times as many songs as Sabrina, who has 120 fewer than Elena. If Pete has 360 songs, how many does Elena have?
25.
A student won 300 of 500 games, then won the next $x$ games. He has now won 80% overall. Find $x$ .
26.
Three consecutive integers sum to $120$ . Find them.
27.
Two angles in a triangle are $(2x + 10)°$ and $(3x - 20)°$ , and the third is $90°$ . Find $x$ .
28.
A square has perimeter $4(x + 3)$ cm. Find $x$ when the perimeter is 32 cm.
29.
Solve $5x + 6 = 3x - 4$ where this gives a negative solution.
30.
I think of a number. I double it and add 5. I then triple the result and subtract 2. The result is 28. Find my number.

PlatinumQuestions 31–40

31.
Solve $\dfrac{x + {a}}{{b}} = \dfrac{x - {c}}{{d}}$ .
32.
Solve $\dfrac{2x + 1}{3} = \dfrac{x - 2}{2}$ .
33.
A laptop costs $x$ chf. The shop applies a 25% discount, then adds 7.7% VAT. The final price is 807.75 chf. Find $x$ .
34.
Two pens and three pencils cost 4.50 chf. One pen and two pencils cost 2.70 chf. Find the cost of each item.
35.
A man is 4 times his son's age now. In 4 years he will be 3 times. Find their current ages.
36.
Solve $\dfrac{1}{x} + \dfrac{1}{2x} = \dfrac{3}{4}$ .
37.
Two consecutive integers have a product of 132. Find them by setting up and solving an equation.
38.
A bottle holds 1.5 L of squash mix at concentration $x$ % sugar. Adding 0.5 L of water reduces concentration to 9%. Find $x$ .
39.
Solve $5 - 2(3x - 4) = 7x - (x + 1)$ .
40.
A rectangle has length $(2x + 1)$ and width $x$ . Its area equals its perimeter. Find $x$ .