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0580/42 Feb/Mar 2024, Question 1: Calculating with Bounds

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 12 marks

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The question, in short

Work through grocery pricing and ratio problems: find a shopping cost, use a 11:8:6 mass ratio, apply a profit rate, reverse a percentage reduction, and bound a bag count.

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

Part (a) · 2 marks

Find the total amount paid for 3 kg of mushrooms at $1.04 per kg plus 4 kg of carrots at $1.28 per kg.

  1. 13 × 1.04 + 4 × 1.28 = 3.12 + 5.12
  2. 2= $8.24

Answer8.24

Part (bi) · 2 marks

Express the mushroom mass as a percentage of the combined mass using the ratio 11:8:6.

  1. 1Total parts = 11 + 8 + 6 = 25
  2. 28/25 × 100 = 32%

Answer32

Part (bii) · 2 marks

Given 1500 kg total, determine how many kilograms of carrots are sold.

  1. 1Total parts = 11 + 8 + 6 = 25
  2. 2One part = 1500 ÷ 25 = 60 kg
  3. 3Carrots = 6 × 60 = 360 kg

Answer360

Part (biii) · 1 mark

Using 360 kg of carrots and $0.75 profit per kg, find the carrot profit.

  1. 1Profit = 0.75 × 360 = $270

Answer270

Part (biv) · 2 marks

After an 8% price cut a kilogram of potatoes costs $1.15; work out the price before the cut.

  1. 1x × (1 − 8/100) = 1.15
  2. 2x = 1.15 ÷ 0.92 = $1.25

Answer1.25

Part (c) · 3 marks

With 620 kg of onions and 5 kg per bag, both rounded, find the largest possible number of bags.

  1. 1Upper bound of onions = 620 + 10 = 630 kg
  2. 2Lower bound of a bag = 5 − 0.5 = 4.5 kg
  3. 3Upper bound of bags = 630 ÷ 4.5 = 140

Answer140

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