GCSE OCR Maths 3D trigonometry: Mr and Mrs Wilde have five child

Mr and Mrs Wilde have five children who are all different ages - OCR - GCSE Maths - Question 10 - 2019 - Paper 1

Question 10

Mr and Mrs Wilde have five children who are all different ages. - The mean age is 6.4. - The range is 9. - The median is 6. - The oldest child is 12. Work out the ... show full transcript

Worked Solution & Example Answer:Mr and Mrs Wilde have five children who are all different ages - OCR - GCSE Maths - Question 10 - 2019 - Paper 1

Step 1

Determine the total age based on mean age

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Answer

To find the total age of the five children, we use the mean age. The mean age is given as 6.4, therefore:

ext{Total Age} = ext{Mean Age} imes ext{Number of Children} = 6.4 imes 5 = 32.

Step 2

Identify the oldest child's age and calculate necessary ages

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Answer

The oldest child is 12 years old. Given that the range is 9, the youngest child's age can be found as follows:

If the oldest is 12, then:

ext{Youngest Age} = ext{Oldest Age} - ext{Range} = 12 - 9 = 3.

So the youngest child's age is 3.

Step 3

Identify the median and remaining ages

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Answer

The median age of the five children is 6. This means that when the ages are ordered from youngest to oldest, the third child must be 6. Therefore, we have the following ages so far:

Youngest: 3
Unknown
Median: 6
Unknown
Oldest: 12

To reach a total age of 32, we need to determine two more ages (let's call them x and y) that fit between 3 and 12, and satisfy:

x + y + 3 + 6 + 12 = 32.

This simplifies to:

x + y + 21 = 32 \Rightarrow x + y = 11.

Step 4

Finding valid ages for x and y

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Answer

The values of x and y must be distinct whole numbers, both greater than 6 and less than 12. The only pairs that satisfy this while also being distinct are (5, 7) or (7, 5).

Thus, we can conclude the ages are:

Youngest: 3
5
Median: 6
7
Oldest: 12

Therefore, the ages arranged from youngest to oldest are: 3, 5, 6, 7, 12.

Mr and Mrs Wilde have five children who are all different ages - OCR - GCSE Maths - Question 10 - 2019 - Paper 1

Worked Solution & Example Answer:Mr and Mrs Wilde have five children who are all different ages - OCR - GCSE Maths - Question 10 - 2019 - Paper 1

Determine the total age based on mean age

Identify the oldest child's age and calculate necessary ages

Identify the median and remaining ages

Finding valid ages for x and y

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