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0580/31 May/Jun 2024, Question 1: Earnings and Deductions

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 15 marks

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The question, in short

Solve a set of cinema-related money, seat, time and pay problems using given prices, percentages and a weekly hours table.

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

Part (ai) · 1 mark

Find the total cost of 4 tickets at $6.30 each.

  1. 14 × 6.30 = 25.20
  2. 2$25.20

Answer25.20

Part (aii) · 2 marks

With 10 tickets sold for the price of 9, find how much each of 10 people pays.

  1. 1Cost of 9 tickets = 9 × 6.30 = 56.70
  2. 2Each person pays 56.70 ÷ 10 = 5.67
  3. 3$5.67

Answer5.67

Part (bi) · 1 mark

Given 650 seats with 26 per row, find the number of rows.

  1. 1650 ÷ 26 = 25 rows

Answer25

Part (bii) · 2 marks

Given 84% of seats are occupied, find how many seats are not occupied.

  1. 1Not occupied = 100% − 84% = 16%
  2. 216% of 650 = 0.16 × 650 = 104

Answer104

Part (c) · 3 marks

Popcorn costs twice water; change from $10 is $3.55. Find the cost of each item.

  1. 1Total spent = 10 − 3.55 = 6.45
  2. 2Popcorn + water = 2w + w = 3w = 6.45
  3. 3w = 6.45 ÷ 3 = 2.15
  4. 4Popcorn = 2 × 2.15 = 4.30
  5. 5Popcorn $4.30, water $2.15

AnswerBag of popcorn $4.30, bottle of water $2.15

Part (di) · 1 mark

Convert 155 minutes into hours and minutes.

  1. 1155 = 120 + 35
  2. 22 hours 35 minutes

Answer2 hours 35 minutes

Part (dii) · 1 mark

A film starts at 14 45 and lasts 2 hours 20 minutes; find its finishing time.

  1. 114 45 + 2 hours = 16 45
  2. 216 45 + 20 minutes = 17 05

Answer17 05

Part (e) · 4 marks

Using the weekly hours table and pay rates before and after 18 00, find Trevor's total weekly pay.

  1. 1Hours before 18 00: 5.5 + 5.5 + 5 = 16 h
  2. 216 × 11.50 = 184
  3. 3Hours after 18 00: 4 + 4 = 8 h
  4. 4Rate after 18 00 = 11.50 × 1.3 = 14.95
  5. 58 × 14.95 = 119.60
  6. 6Total = 184 + 119.60 = $303.60

Answer303.60

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