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On a plane, $ rac{2}{5}$ of the passengers were British - OCR - GCSE Maths - Question 10 - 2019 - Paper 1
Question 10
On a plane, $ rac{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 number of p... show full transcript
Worked Solution & Example Answer:On a plane, $ rac{2}{5}$ of the passengers were British - OCR - GCSE Maths - Question 10 - 2019 - Paper 1
Step 1
Step 2
Determine the total number of British men
Answer
We know that 30% of the British passengers were men. Therefore, we can express this as:
[ \text{Number of British men} = 0.3 \times \left(\frac{2}{5} x\right) ]
We also know that this equals 36:
[ 0.3 \times \left(\frac{2}{5} x\right) = 36 ]
Step 3
Solve for the total number of passengers
Answer
To isolate ( x ), we solve the equation:
[ 0.3 \times \left(\frac{2}{5} x\right) = 36 ]
Multiplying both sides by ( \frac{5}{2} ) and then by ( \frac{1}{0.3} ):
[ x = \frac{36 \times 5}{2 \times 0.3} ]
[ x = \frac{180}{0.6} ]
[ x = 300 ]
Thus, the total number of passengers on the plane is ( 300 ).