Question

age problem algebra

Answer 1

Sure! Age problems in algebra typically involve understanding relationships between the ages of different people at various points in time. Here's a common format for these problems, along with a step-by-step solution.

### Example Problem:

**Problem:**
John is 4 years older than Maria. In 6 years, the sum of their ages will be 50. How old are John and Maria now?

### Step-by-step Solution:

1. **Define the variables:**
- Let Maria's current age be \( M \).
- Then, John's current age will be \( J = M + 4 \).

2. **Set up the equation based on future ages:**
- In 6 years, Maria's age will be \( M + 6 \).
- In 6 years, John's age will be \( J + 6 = (M + 4) + 6 = M + 10 \).
- The problem states that the sum of their ages in 6 years will be 50:
\[
(M + 6) + (M + 10) = 50
\]

3. **Simplify the equation:**
\[
2M + 16 = 50
\]

4. **Solve for \( M \):**
- Subtract 16 from both sides:
\[
2M = 34
\]
- Divide by 2:
\[
M = 17
\]

5. **Find John's current age:**
- Substitute \( M \) back to find \( J \):
\[
J = M + 4 = 17 + 4 = 21
\]

### Conclusion:
- Maria is currently 17 years old.
- John is currently 21 years old.

If you have a specific age problem you'd like help with, feel free to provide the details!