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

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.

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:

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

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.