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Let's define the variables for the ages of each person in the problem:

- Let \( J \) be Jane's age.
- Let \( R \) be Ranjit's age.
- Let \( A \) be Anita's age.
- Let \( B \) be the boy's age (he hasn't been named yet).

Now, let's work through the information in each speech bubble:

1. **Jane** says: "The sum of mine and Ranjit's ages is 22."  
   This gives us the equation:  
   \[
   J + R = 22
   \]

2. **Ranjit** says: "The difference between mine and Jane's ages is 4."  
   This gives the equation:  
   \[
   |J - R| = 4
   \]
   (We will check which of \( J > R \) or \( R > J \) makes sense later.)

3. **The Boy** says: "I am 3 years younger than Anita and Jane."  
   This gives us the relation:  
   \[
   B = J - 3 = A - 3
   \]

4. **Anita** says: "I am the same age as Jane and we are the oldest."  
   Thus, we have:  
   \[
   A = J
   \]

Now, let's solve the system of equations:

- From **Anita's** statement, \( A = J \), so we can substitute \( A \) for \( J \) in all the equations.
- The **Boy**'s statement becomes \( B = J - 3 \).
- From **Jane**'s statement: \( J + R = 22 \).
- From **Ranjit**'s statement: \( J - R = 4 \) (since \( J > R \)).

We can now solve these equations step by step:

1. From \( J - R = 4 \), we can express \( R \) as:
   \[
   R = J - 4
   \]

2. Substituting \( R = J - 4 \) into \( J + R = 22 \):
   \[
   J + (J - 4) = 22
   \]
   \[
   2J - 4 = 22
   \]
   \[
   2J = 26
   \]
   \[
   J = 13
   \]

3. Now that we know \( J = 13 \), we can find \( R \):
   \[
   R = J - 4 = 13 - 4 = 9
   \]

4. From the **Boy's** statement, \( B = J - 3 \), so:
   \[
   B = 13 - 3 = 10
   \]

Thus, the ages of the characters are:

- Jane and Anita are both 13 years old.
- Ranjit is 9 years old.
- The Boy is 10 years old.

Would you like more details on any step, or have any questions?

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Here are 5 related questions for you to explore:

1. How can we verify that the difference between Jane and Ranjit's ages is exactly 4?
2. If Jane were 2 years older, how would that affect Ranjit’s and the Boy's ages?
3. What if the sum of Jane and Ranjit's ages were different? How would the solution change?
4. Can we create a similar problem with different ages for each character?
5. How would the problem change if Ranjit were the same age as the Boy?

**Tip:** When solving word problems, translating each sentence into an equation can simplify the process of finding solutions!

Can you work out the characters' ages based on the clues provided by Jane, Ranjit, Anita, and the boy?

Work out the ages of Jane, Ranjit, Anita, and the boy using algebraic equations. The clues include the sum and difference of ages, and relations among the characters. Suitable for students in Grades 6-8.

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