https://file.aiquickdraw.com/mathbot/file/17276204991877ldzb5a5.jpg

Let's define variables to represent the ages of the characters based on the clues in the image:

- Let the first character (blonde) be \( A \).
- The second character (wearing a turban) is \( R \) (Ranjit).
- The third character (green shirt) is \( B \).
- The fourth character (brown hair) is \( J \) (Jane).

From the image, we have the following information:

1. \( A + R = 22 \)
2. \( R - J = 4 \) (Ranjit is 4 years older than Jane)
3. \( B = J - 3 \) (The third character is 3 years younger than Jane and Anita)
4. \( A = J \) (Anita is the same age as Jane, and they are the oldest)

Now let's solve these equations step-by-step to find their ages.

### Step 1: Substitute \( A = J \) in equation 1
Using \( A = J \) in equation 1:
\[
J + R = 22
\]
So, we now have:
\[
J + R = 22 \quad \text{(i)}
\]
and
\[
R - J = 4 \quad \text{(ii)}
\]

### Step 2: Solve for \( R \) and \( J \)
We can add equations (i) and (ii):
\[
(J + R) + (R - J) = 22 + 4
\]
\[
2R = 26
\]
\[
R = 13
\]

Substitute \( R = 13 \) into equation (ii):
\[
13 - J = 4
\]
\[
J = 9
\]

### Step 3: Find the remaining ages
- \( A = J = 9 \) (since Anita is the same age as Jane)
- \( B = J - 3 = 9 - 3 = 6 \)

Thus, the ages are:
- Anita (A) = 9 years old
- Ranjit (R) = 13 years old
- The third character (B) = 6 years old
- Jane (J) = 9 years old

Would you like further details, or do you have any questions?

Here are 5 questions to deepen understanding:
1. How would the solution change if Ranjit were younger than Jane?
2. What if the sum of Anita and Ranjit’s ages was different, say 20 instead of 22?
3. How could we set up the system of equations if two other people had the same age?
4. How would you solve this problem if you only knew the age differences?
5. Could you solve this problem graphically using a number line?

**Tip:** Always double-check the relationships between variables to ensure the constraints are applied correctly!

Can you work out the characters' ages based on the clues provided in the image?

Learn how to solve a fun age puzzle using algebra. Follow a step-by-step solution that involves forming equations and solving for the ages of the characters Anita, Ranjit, and Jane using substitution and addition methods. Suitable for students in Grades 5-7.

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