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The problem asks to define a variable and then write and solve an equation for Todd and Jamal's ages, given the following information:

- Todd is 10 years older than Jamal.
- The sum of their ages is 64.

### Step 1: Define a variable
Let \( x \) be Jamal's age.

### Step 2: Express Todd's age in terms of Jamal's age
Since Todd is 10 years older than Jamal, Todd's age is \( x + 10 \).

### Step 3: Set up the equation
We are told that the sum of their ages is 64, so we can write the equation:
\[
x + (x + 10) = 64
\]

### Step 4: Solve the equation
Simplify the equation:
\[
2x + 10 = 64
\]
Subtract 10 from both sides:
\[
2x = 54
\]
Divide by 2:
\[
x = 27
\]

So, Jamal is 27 years old.

### Step 5: Find Todd's age
Todd's age is \( x + 10 = 27 + 10 = 37 \).

### Final Answer
Jamal is 27 years old, and Todd is 37 years old.

Do you want more details, or have any questions? 

Here are some related questions to deepen your understanding:
1. What would the equation look like if Todd was 5 years older instead of 10?
2. If the sum of their ages was 70 instead of 64, how would the solution change?
3. How would the problem change if Jamal was the one who was 10 years older than Todd?
4. Can you write a similar problem where the difference in ages is 15 years instead of 10?
5. How would you verify that the solution is correct?

**Tip:** When solving age-related word problems, always double-check the relationships between the variables to avoid errors in setting up the equation.

Todd is 10 years older than Jamal. The sum of their ages is 64. How old are Todd and Jamal?

Learn how to solve an age-related algebra problem where Todd is 10 years older than Jamal, and the sum of their ages is 64. A step-by-step breakdown covers linear equations and how to solve for both ages. Suitable for students in Grades 6-8.

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