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There is a total of 250 men, women and children on a train - OCR - GCSE Maths - Question 9 - 2017 - Paper 1

Question 9

There is a total of 250 men, women and children on a train. The ratio of men to women is 4 : 5. The ratio of women to children is 10 : 7. How many men are on the tr... show full transcript

Worked Solution & Example Answer:There is a total of 250 men, women and children on a train - OCR - GCSE Maths - Question 9 - 2017 - Paper 1

Step 1

Calculate the Total Ratio of Men, Women, and Children

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Answer

The ratio of men to women is given as 4:5. Let the number of men be 4x and the number of women be 5x.

Next, we know the ratio of women to children is 10:7. If we let the number of women be 10y and the number of children be 7y, we can equate the two expressions for women:

$5x = 10y$

From this, we can simplify to find the relationship between x and y:

$x = 2y$

Step 2

Express Total Count in Terms of y

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Answer

Next, we can express the total number of people (250) in terms of y:

The number of men = 4x = 4(2y) = 8y, The number of women = 10y, The number of children = 7y.

Thus, the total can be written as:

$8y + 10y + 7y = 250$

This simplifies to:

$25y = 250$

So, solving for y:

$y = 10$

Step 3

Calculate the Number of Men

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Answer

Now, we can find the number of men:

Using the previously calculated expression for men:

$Men = 8y = 8(10) = 80$

Therefore, the number of men on the train is 80.

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