Let's break down the problem step by step.
1. Define Variables:
- Let the son's age be denoted as [tex]\( s \)[/tex].
- Since Kate is three times as old as her son, Kate's age can be expressed as [tex]\( 3s \)[/tex].
2. Set Up the Equation:
- We are given that Kate is 30 years older than her son.
- Therefore, we can write the equation:
[tex]\[
3s = s + 30
\][/tex]
3. Solve for [tex]\( s \)[/tex]:
- First, let's isolate [tex]\( s \)[/tex] on one side of the equation:
[tex]\[
3s - s = 30
\][/tex]
- Simplify the equation:
[tex]\[
2s = 30
\][/tex]
- Solve for [tex]\( s \)[/tex]:
[tex]\[
s = \frac{30}{2}
\][/tex]
[tex]\[
s = 15
\][/tex]
4. Find Kate's Age:
- Since Kate's age is three times the son's age:
[tex]\[
\text{Kate's age} = 3s = 3 \times 15 = 45
\][/tex]
Thus, the son's age is 15 years old, and Kate's age is 45 years old.
