GCSE OCR Maths Percentages: The ratio 45 minutes to 3 hours

The ratio 45 minutes to 3 hours 45 minutes can be written in the form 1 : n - OCR - GCSE Maths - Question 3 - 2020 - Paper 1

Question 3

The ratio 45 minutes to 3 hours 45 minutes can be written in the form 1 : n. Find the value of n. Reece and Sarah share some money in the ratio 9 : 16. Reece says... show full transcript

Worked Solution & Example Answer:The ratio 45 minutes to 3 hours 45 minutes can be written in the form 1 : n - OCR - GCSE Maths - Question 3 - 2020 - Paper 1

Step 1

Find the value of n

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Answer

To find the value of n in the ratio 45 minutes to 3 hours 45 minutes, we first convert everything into the same units.

Convert 3 hours 45 minutes into minutes: 3 hours = 3 × 60 = 180 minutes, so 3 hours 45 minutes = 180 + 45 = 225 minutes.
Now we can express the ratio as:

$45 : 225$
Simplify the ratio by dividing both sides by 45:

$\frac{45}{45} : \frac{225}{45} = 1 : 5$
Thus, we have the ratio in the form 1 : n, where n = 5.

Step 2

Show that Sarah gets more than 60% of this money

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Answer

First, let's denote the total parts in the ratio 9 : 16. Total parts = 9 + 16 = 25 parts.
The share of Sarah = 16 parts.
To find out what percentage of the total money Sarah gets, we can use the formula:

$\text{Percentage} = \left( \frac{\text{Sarah's share}}{\text{Total share}} \right) \times 100 = \left( \frac{16}{25} \right) \times 100$
Calculating this gives:

$\left( \frac{16}{25} \right) \times 100 = 64\%$
Since 64% is greater than 60%, Reece's statement that Sarah gets more than 60% of the money is correct.

The ratio 45 minutes to 3 hours 45 minutes can be written in the form 1 : n - OCR - GCSE Maths - Question 3 - 2020 - Paper 1

Worked Solution & Example Answer:The ratio 45 minutes to 3 hours 45 minutes can be written in the form 1 : n - OCR - GCSE Maths - Question 3 - 2020 - Paper 1

Find the value of n

Show that Sarah gets more than 60% of this money

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