On a plane, \frac{2}{5} of the passengers were British.\n30% of the British passengers were men.\nThere were 36 British men on the plane.\nFind the total number of passengers on the plane. - OCR - GCSE Maths - Question 10 - 2019 - Paper 1
Question 10
On a plane, \frac{2}{5} of the passengers were British.\n30% of the British passengers were men.\nThere were 36 British men on the plane.\nFind the total number of p... show full transcript
Worked Solution & Example Answer:On a plane, \frac{2}{5} of the passengers were British.\n30% of the British passengers were men.\nThere were 36 British men on the plane.\nFind the total number of passengers on the plane. - OCR - GCSE Maths - Question 10 - 2019 - Paper 1
Step 1
Find the number of British passengers
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Answer
Let the total number of passengers be represented by ( x ). According to the information given, ( \frac{2}{5} ) of the passengers are British. Therefore, the number of British passengers is ( \frac{2}{5}x ).
Step 2
Determine the number of British men
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Answer
We know that 30% of the British passengers are men. Hence, the number of British men can be expressed as ( 0.30 \times \frac{2}{5}x = \frac{3}{50}x ).
Step 3
Set up the equation based on the number of British men
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Answer
Given that there are 36 British men, we can set the equation ( \frac{3}{50}x = 36 ).
Step 4
Solve for x
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Answer
To find ( x ), multiply both sides by 50 to eliminate the fraction:
[ 3x = 36 \times 50 ]
[ 3x = 1800 ]
Now, divide by 3:
[ x = \frac{1800}{3} = 600 ].
Step 5
Conclusion
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Answer
Thus, the total number of passengers on the plane is ( 600 ).
