Lemmara logoLemmaraWorked solution

0580/42 Oct/Nov 2022, Question 1: Constructing Equations

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 16 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Football club ticket and attendance problems: use ratios, percentage decrease, percentage of total, exponential growth, and form and solve an equation in x.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (ai) · 2 marks

Seated to standing ticket ratio is 5:3 and a standing ticket costs $45; find the seated ticket cost.

  1. 1Seated = 45 ÷ 3 × 5
  2. 2= $75

Answer75

Part (aii) · 2 marks

Player value is $2.65 million and falls by 12%; find the 2022 value.

  1. 1Value = 2.65 × (1 − 12/100) = 2.65 × 0.88
  2. 2= $2.332 million

Answer2.332

Part (aiii) · 2 marks

Attendance 1455 is 6.25% of stadium capacity; find the total allowed.

  1. 16.25/100 × x = 1455
  2. 2x = 1455 ÷ 0.0625 = 23280

Answer23280

Part (aiv) · 3 marks

Attendance grows 4% yearly from 2016 to 2019, reaching 1631; find the 2016 attendance.

  1. 11631 = k × (1 + 4/100)³
  2. 2k = 1631 ÷ 1.04³ = 1631 ÷ 1.124864
  3. 3= 1449.95… ≈ 1450

Answer1450 or 1449 to 1450

Part (bi) · 1 mark

Family to individual tickets ratio is 2:7 with x family tickets; write individual tickets in terms of x.

  1. 1family : individual = 2 : 7, so individual = x ÷ 2 × 7
  2. 2= (7x)/2

Answer(7x)/2

Part (bii) · 2 marks

Complete the table: 2018 family x, 2019 family up 12, individual down 26, using x expressions.

  1. 1From part (b)(i): family : individual = 2 : 7, so individual tickets in 2018 = (7/2) × x = 7x/2
  2. 22019 family tickets: family increases by 12, so x + 12
  3. 32019 individual tickets: individual decreases by 26, so 7x/2 − 26

Answer2019: Family tickets x + 12, Individual tickets (7x)/2 − 26

Part (biii) · 4 marks

In 2019 individual tickets are 3 times family tickets; write and solve an equation in x for 2018 family tickets.

  1. 1(7x)/2 − 26 = 3(x + 12)
  2. 27x − 52 = 6x + 72
  3. 3x = 124

Answer(7x)/2 − 26 = 3(x + 12), x = 124

Stuck on a step? Read the free lesson: Constructing Equations

Practise more constructing equations questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on constructing equations

Also searched as: 0580/42/O/N/22 · 0580_w22_qp_42 · 0580 w22 42 · question 1.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.