Question

The sum of ages of 5 children born at the intervals of 3 years each is 60 years. What is the age of the youngest child?
4
6
5
18

Answer 1

Let the age of the youngest child be \( x \). Since the children are born at intervals of 3 years, their ages can be represented as follows:

- Youngest child: \( x \)
- Second child: \( x + 3 \)
- Third child: \( x + 6 \)
- Fourth child: \( x + 9 \)
- Fifth child: \( x + 12 \)

The sum of their ages can be written as:

\[
x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 60
\]

Simplifying the left side, we get:

\[
5x + (3 + 6 + 9 + 12) = 60
\]

Calculating the sum of the constants:

\[
3 + 6 + 9 + 12 = 30
\]

The equation now looks like:

\[
5x + 30 = 60
\]

Subtracting 30 from both sides gives:

\[
5x = 30
\]

Dividing by 5:

\[
x = 6
\]

Thus, the age of the youngest child is \( \boxed{6} \).