Let's carefully analyze the information provided in the question:
- Luke's age is defined in relation to Sydney's age, [tex]\( s \)[/tex].
- Specifically, Luke's age is 5 years younger than 3 times Sydney's age.
Now, let's think about what [tex]\( 3s \)[/tex] represents in this context:
1. [tex]\( s \)[/tex] represents Sydney's age.
2. When we multiply Sydney's age [tex]\( s \)[/tex] by 3, we get [tex]\( 3s \)[/tex]. This means "three times Sydney's age."
Therefore, [tex]\( 3s \)[/tex] represents three times Sydney's age, not Luke's age or Sydney's age itself. It's also not three times Luke's age since Luke's age involves subtracting 5 from [tex]\( 3s \)[/tex].
Hence, the correct answer is:
three times Sydney's age
