Tom's age is thrice the age of Tim, Tim's age is four times the age of Ron and Ron's age is twice the age of Lily. If the mean of the ages of Tom, Tim, Ron and Lily is 35 years, then the present age of Tim is
years.

Let's solve the problem step by step.

Let:
- Lily's age be \( L \) years.
- Ron's age be \( R \) years.
- Tim's age be \( T \) years.
- Tom's age be \( M \) years.

Given the relationships:
1. \( R = 2L \) (Ron is twice the age of Lily)
2. \( T = 4R \) (Tim is four times the age of Ron)
3. \( M = 3T \) (Tom is thrice the age of Tim)

We also know the mean age of the four people is 35 years:
\[
\frac{M + T + R + L}{4} = 35
\]

First, express all ages in terms of \( L \):
1. \( R = 2L \)
2. \( T = 4R = 4(2L) = 8L \)
3. \( M = 3T = 3(8L) = 24L \)

Now, substitute these into the mean equation:
\[
\frac{M + T + R + L}{4} = 35
\]
\[
\frac{24L + 8L + 2L + L}{4} = 35
\]
\[
\frac{35L}{4} = 35
\]

Solve for \( L \):
\[
35L = 140
\]
\[
L = 4
\]

Now, find the ages:
- Lily's age \( L = 4 \) years.
- Ron's age \( R = 2L = 2(4) = 8 \) years.
- Tim's age \( T = 8L = 8(4) = 32 \) years.
- Tom's age \( M = 24L = 24(4) = 96 \) years.

Therefore, the present age of Tim is \( 32 \) years.

Would you like more details or have any questions?

Here are 5 questions for you to ask:
1. How do you solve systems of equations?
2. What are some common age-related math problems?
3. How can I check my work when solving word problems?
4. What are the steps to solve a word problem involving proportions?
5. Can you explain how to find the mean of a set of numbers?

**Tip:** When dealing with word problems, it's helpful to define all the variables clearly and write down the given relationships before attempting to solve the problem.

Discover how to find Tim's age in a problem involving relationships between ages of Tom, Tim, Ron, and Lily. This problem includes calculating mean age and solving equations step-by-step. Suitable for students in Grades 7-9.

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