Module 8 · Answers
Answers & working
Workings shown so you can see where each answer comes from.
Section A — Easy
01
(a) 2 : 3 (b) 4 : 3 (c) 2 : 3 : 5
02
£18 and £27
5 parts; 45 ÷ 5 = 9. Shares: 2 × 9 = 18, 3 × 9 = 27.
03
£2.10
1 apple = 1.20 ÷ 4 = £0.30. 7 × 0.30 = 2.10.
04
(a) Mean = 8 (b) Median = 7 (c) Mode = 7 (d) Range = 9
Mean: (4+7+7+9+13)/5 = 40/5.
Range: 13 − 4.
Range: 13 − 4.
05
120°
(12 ÷ 36) × 360 = 120.
Section B — Medium
06
60 and 84
Total parts = 12; 144 ÷ 12 = 12. Shares: 5 × 12, 7 × 12.
07
Cereal B
A: 240 ÷ 400 = 0.60p/g.
B: 330 ÷ 600 = 0.55p/g.
B costs less per gram.
B: 330 ÷ 600 = 0.55p/g.
B costs less per gram.
08
Mean = 1.85
Σf = 2 + 5 + 8 + 4 + 1 = 20.
Σfx = 0 + 5 + 16 + 12 + 4 = 37.
Mean = 37 ÷ 20 = 1.85.
Σfx = 0 + 5 + 16 + 12 + 4 = 37.
Mean = 37 ÷ 20 = 1.85.
09
(a) 24 km (b) 15 miles
(a) 15 × 8/5 = 24.
(b) 24 × 5/8 = 15.
(b) 24 × 5/8 = 15.
10
Walk 150°, Cycle 90°, Bus 75°, Drive 45°
Each angle = (frequency ÷ 120) × 360 = frequency × 3.
Section C — Hard
11
£50 000
Difference between eldest (5 parts) and youngest (2 parts) = 3 parts = £15 000.
1 part = £5 000. Total = 10 parts = £50 000.
1 part = £5 000. Total = 10 parts = £50 000.
12
f = 7
Σfx = 6 + 15 + 16 + 5f + 12 = 49 + 5f.
Σf = 14 + f.
(49 + 5f) ÷ (14 + f) = 4
49 + 5f = 56 + 4f
f = 7.
Σf = 14 + f.
(49 + 5f) ÷ (14 + f) = 4
49 + 5f = 56 + 4f
f = 7.
13
560g flour
320 ÷ 4 = 80g per person. 7 × 80 = 560.
14
16 students
(96 ÷ 360) × 60 = 16.
15
24 and 42
Let the numbers be 4k and 7k.
(4k + 6) / (7k + 6) = 5 / 8
8(4k + 6) = 5(7k + 6)
32k + 48 = 35k + 30
3k = 18 → k = 6.
Numbers: 24 and 42. Check: 30/48 = 5/8 ✓.
(4k + 6) / (7k + 6) = 5 / 8
8(4k + 6) = 5(7k + 6)
32k + 48 = 35k + 30
3k = 18 → k = 6.
Numbers: 24 and 42. Check: 30/48 = 5/8 ✓.