# The sum of ages of 5 children born at intervals of 3 years each is 50 years. What is the age of the youngest child?

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Let x = the youngest child. Each of the other four children will then be x+3, x+6, x+9, x+12. We know that the **sum** of their ages is 50 so we can form an equation:

x+(x+3)+(x+6)+(x+9)+(x+12) = 50

`therefore` 5x+30 = 50

`therefore` 5x=50-30

`therefore x=20/5`

`therefore x=4`

**Therefore the youngest child is 4 years old. **

The ages of the children are in arithmetic progression.

Let the ages of the children in years be (n-6),(n-3), (n), (n+3), (n+6), which satisfies the given condition.

Adding the ages, we get,

`(n-6)+(n-3)+(n)+(n+3)+(n+6) = 50`

`rArr 5n = 50`

`rArr n = 10`

It is obvious that smallest age `= (n-6)`

`= (10 - 6)`

`= 4 years`

x+(x+3)+(x+6)+(x+9)+(x+12) = 50

combine like terms:

5x + 30 = 50

Subtract the 30:

5x = 20

divide by 5

x = 4

the youngest child is 4

x+(x+3)+(x+6)+(x+9)+(x+12) = 50

combine like terms:

x+x+x+x+x = 5x

3 + 6 + 9 + 12

5x + 30 = 50

Subtract the 30:

5x = 20

divide 5x and 20 by 5

x = 4

the youngest child is 4