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Festival A will be in a rectangular field with an area of 80000m² The greatest number of people allowed to attend Festival A is 425 Festival B will be in a rectangular field 700m by 2000m.. - Edexcel - GCSE Maths - Question 4 - 2022 - Paper 2
Question 4
Festival A will be in a rectangular field with an area of 80000m² The greatest number of people allowed to attend Festival A is 425 Festival B will be in a rectangu... show full transcript
Worked Solution & Example Answer:Festival A will be in a rectangular field with an area of 80000m² The greatest number of people allowed to attend Festival A is 425 Festival B will be in a rectangular field 700m by 2000m.. - Edexcel - GCSE Maths - Question 4 - 2022 - Paper 2
Step 1
How much greater?
Answer
To determine how much greater the area allowed per person is for Festival B compared to Festival A, we first need to calculate the area available per person for each festival.
Step 1: Calculate the area per person for Festival A.
The total area for Festival A is 80000m² and the maximum number of people allowed is 425.
a_{A} = \frac{80000}{425} \approx 188.24 , ext{m² per person}
Step 2: Calculate the area per person for Festival B.
First, we find the area of Festival B:
Area = Length × Width = 700m × 2000m = 1400000m²
Now, divide this area by the maximum number of people allowed:
a_{B} = \frac{1400000}{6750} \approx 207.41 , ext{m² per person}
Step 3: Find the difference in area per person between Festival B and Festival A.
Difference = a_{B} - a_{A} = 207.41 - 188.24 \approx 19.17 , ext{m²}
Finally, rounding to the nearest whole number, the area per person for Festival B is greater by approximately 19 m².
Step 2
Explain why Callum's method is wrong.
Answer
Callum's method is incorrect for the following reasons:
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Unit Conversion: Callum inaccurately equates 300 cm² to 3 m² without proper conversion. The correct approach is to recognize that 1 m² = 10000 cm², not 100 cm².
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Calculation Error: When converting cm² to m², you must divide by 10000, not 100. Therefore, 300 cm² is actually ( \frac{300}{10000} = 0.03 , ext{m²} ).
By misunderstanding the relationship between square centimeters and square meters, Callum's conclusion about the equivalence of these areas is flawed. This exemplifies that he failed to square the conversion factor.