At the end of each year, a driver records how many kilometres they have driven. In 2021, they drove 18% more kilometres than in 2020. In 2022, they drove 25% more kilometres than in 2020. In 2022, they drove 3500 km. (a) Kai says I can work out how many kilometres were driven in 2020 by reducing 3500 by 25%. 3500 × 0.75 = 2625 km. Explain why 2625 is not the correct number of kilometres driven in 2020. (b) Calculate the number of kilometres driven in 2021.

GCSE OCR Maths Proportion: At the end of each year, a drive

At the end of each year, a driver records how many kilometres they have driven - OCR - GCSE Maths - Question 23 - 2023 - Paper 3

Question 23

At the end of each year, a driver records how many kilometres they have driven. In 2021, they drove 18% more kilometres than in 2020. In 2022, they drove 25% more k... show full transcript

Worked Solution & Example Answer:At the end of each year, a driver records how many kilometres they have driven - OCR - GCSE Maths - Question 23 - 2023 - Paper 3

Step 1

Explain why 2625 is not the correct number of kilometres driven in 2020.

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Answer

To find the number of kilometres driven in 2020, we need to compute the total distance driven in 2022 backwards considering the increase percentage.

Kai incorrectly assumes that reducing 3500 km by 25% gives the kilometres driven in 2020. However, in reality, 3500 km for 2022 includes a 25% increase from the kilometres driven in 2020.

We need to do the reverse calculation to correctly account for the increase: Let the kilometres driven in 2020 be denoted as x.

The relationship can be expressed as:

$3500 = x + 0.25x$

which simplifies to:

$3500 = 1.25x$

Thus:

$x = \frac{3500}{1.25} = 2800 ext{ km}$

So, 2625 km cannot be correct as it misrepresents the original amount driven in 2020.

Step 2

Calculate the number of kilometres driven in 2021.

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Answer

We have already established that the kilometres driven in 2020 is 2800 km.

To find the distance driven in 2021, we calculate 18% more than the 2020 distance:

$2800 + 0.18 \times 2800 = 2800 + 504 = 3304 ext{ km}$

Therefore, the number of kilometres driven in 2021 is 3304 km.

At the end of each year, a driver records how many kilometres they have driven - OCR - GCSE Maths - Question 23 - 2023 - Paper 3

Worked Solution & Example Answer:At the end of each year, a driver records how many kilometres they have driven - OCR - GCSE Maths - Question 23 - 2023 - Paper 3

Explain why 2625 is not the correct number of kilometres driven in 2020.

Calculate the number of kilometres driven in 2021.

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