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On a plane, \( \frac{2}{5} \) of the passengers were British - OCR - GCSE Maths - Question 19 - 2019 - Paper 1
Question 19
On a plane, \( \frac{2}{5} \) of the passengers were British. 30% of the British passengers were men. There were 36 British men on the plane. Find the total numbe... show full transcript
Worked Solution & Example Answer:On a plane, \( \frac{2}{5} \) of the passengers were British - OCR - GCSE Maths - Question 19 - 2019 - Paper 1
Step 1
Find the total number of British passengers
Answer
Let the total number of passengers on the plane be ( x ).
The number of British passengers is given by:
[ \frac{2}{5}x ]
Since 30% of the British passengers were men and there are 36 British men:
[ 0.3 \times \frac{2}{5}x = 36 ]
Now, solving for ( x ):
[ \frac{2}{5}x = \frac{36}{0.3} ]
Calculating the right side:
[ \frac{36}{0.3} = 120 ]
Thus, we have:
[ \frac{2}{5}x = 120 ]
To find ( x ), multiply both sides by ( \frac{5}{2} ):
[ x = 120 \times \frac{5}{2} = 300 ]