Question

There are six children in a family. Five of them are respectively 2, 6, 8, 12 and 14 years older than the youngest, and the age of each child is a prime number. How old is the youngest?

Answer 1

The youngest is 5 years old

Step-by-step explanation:

The prime numbers are the numbers that have only two factors

1 and itself

Example: 2, 3, 5, 7, 11, 13, 17, 19, 23, .......

There are six children in a family

• Five of them are respectively 2, 6, 8, 12 and 14 years older than the youngest
• The age of each child is a prime number

We need to find the age of the youngest

Assume that the age of the youngest is x years old

∵ The age of the youngest is x years old

∵ The ages of other children are respectively 2, 6, 8, 12 and 14 years

   older than the youngest

∴ The ages of other children are respectively

→ x + 2

→ x + 6

→ x + 8

→ x + 12

→ x + 14

∵ The age of each child is a prime number

- Let us chose x from the list of the prime number above to find the

  correct x which makes all the ages are prime

If x = 2

∵ x + 2 = 2 + 2 = 4 ⇒ not prime

∴ x can not be 2

If x = 3

∵ x + 2 = 3 + 2 = 5 ⇒ prime

∵ x + 6 = 3+ 6 = 9 ⇒ not prime

∴ x can not be 3

If x = 5

∵ x + 2 = 5 + 2 = 7 ⇒ prime

∵ x + 6 = 5 + 6 = 11 ⇒ prime

∵ x + 8 = 5 + 8 = 13 ⇒ prime

∵ x + 12 = 5 + 12 = 17 ⇒ prime

∵ x + 14 = 5 + 14 = 19 ⇒ prime

∴ x can be 5

∵ The ages of the children are 5 , 7 , 11 , 13 , 17 , 19

∵ All the ages are prime numbers

∴ The age of the youngest is 5 years

The youngest is 5 years old

Learn more:

You can learn more about prime numbers in brainly.com/question/4550858

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Answer 2

Answer:

The youngest is 5 years old