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Festival A will be in a rectangular field with an area of 80000 m² - Edexcel - GCSE Maths - Question 5 - 2022 - Paper 2
Question 5
Festival A will be in a rectangular field with an area of 80000 m². The greatest number of people allowed to attend Festival A is 425. Festival B will be in a recta... show full transcript
Worked Solution & Example Answer:Festival A will be in a rectangular field with an area of 80000 m² - Edexcel - GCSE Maths - Question 5 - 2022 - Paper 2
Step 1
How much greater?
Answer
To find the area available per person for each festival:
-
Festival A:
- Area: 80000 m²
- Maximum people: 425
- Area per person = ( \frac{80000}{425} \approx 188.24 , m² )
-
Festival B:
- Dimensions: 700 m x 2000 m
- Area = 700 * 2000 = 1400000 m²
- Maximum people: 6750
- Area per person = ( \frac{1400000}{6750} \approx 207.41 , m² )
-
Comparison:
- Difference in area per person = ( 207.41 - 188.24 \approx 19.17 , m² )
- Rounding to the nearest whole number gives approximately 19 m².
Step 2
Explain why Callum's method is wrong.
Answer
Callum's method is incorrect because:
- He wrongly assumes that to convert cm² to m², you only need to divide by 100. In fact, 1 m = 100 cm, so:
- To convert from cm² to m², you must divide by ( 100^2 = 10000 ).
- Therefore, 300 cm² actually equals ( \frac{300}{10000} = 0.03 , m² ), not 3 m² as he claims.