The product of Tanvy's age (in years) 5 years ago and her age 8 years later is 30. Find her present age.

Explanation

To solve the problem, we will define Tanvi's present age and set up an equation based on the information given.

### Step-by-Step Solution:

1. **Define the variable**: Let Tanvi's present age be \( x \) years.

2. **Express ages in terms of \( x \)**:
- Tanvi's age 5 years ago: \( x - 5 \)
- Tanvi's age 8 years later: \( x + 8 \)

3. **Set up the equation**: According to the problem, the product of her age 5 years ago and her age 8 years later is 30. Therefore, we can write the equation:
\[ (x - 5)(x + 8) = 30 \]

4. **Expand the equation**:
\[ x^2 + 8x - 5x - 40 = 30 \]
Simplifying this gives:
\[ x^2 + 3x - 40 = 30 \]

5. **Rearrange the equation**: Move 30 to the left side:
\[ x^2 + 3x - 40 - 30 = 0 \]
This simplifies to:
\[ x^2 + 3x - 70 = 0 \]

6. **Factor the quadratic equation**: We need to find two numbers that multiply to -70 and add to 3. The numbers are 10 and -7. Thus, we can factor the equation as:
\[ (x - 7)(x + 10) = 0 \]

7. **Solve for \( x \)**: Set each factor to zero:
- \( x - 7 = 0 \) → \( x = 7 \)
- \( x + 10 = 0 \) → \( x = -10 \) (not valid as age cannot be negative)

8. **Conclusion**: The only valid solution is:
\[ x = 7 \]
Therefore, Tanvi's present age is **7 years**.