At her birthday​ party, Ms. Willow would not give her age directly. She​ said, 'If you add the year of my birth to this​ year, subtract the year of my 15th birthday and the year of my 45th ​birthday, and then add my present​ age, the result is 60​.'

We can set up an equation to represent the information Ms. Willow provided.

Let:
- \( Y_b \) be the year of Ms. Willow's birth,
- \( A \) be her current age,
- The current year is \( Y_c \).

From the problem, Ms. Willow said:

\[
Y_b + Y_c - (Y_b + 15) - (Y_b + 45) + A = 60
\]

### Simplifying the expression step by step:
1. \( Y_b + Y_c - Y_b - 15 - Y_b - 45 + A = 60 \)
2. Combine like terms:
\[
Y_c - Y_b - Y_b - 15 - 45 + A = 60
\]
3. Further simplification:
\[
Y_c - 2Y_b - 60 + A = 60
\]
4. Add 60 to both sides:
\[
Y_c - 2Y_b + A = 120
\]

This is the equation that relates the current year \( Y_c \), the year of Ms. Willow's birth \( Y_b \), and her current age \( A \).

Now, since \( A = Y_c - Y_b \) (because age is the difference between the current year and birth year), we substitute \( A \) into the equation:

\[
Y_c - 2Y_b + (Y_c - Y_b) = 120
\]

Simplifying:

\[
Y_c - 2Y_b + Y_c - Y_b = 120
\]

Combine like terms:

\[
2Y_c - 3Y_b = 120
\]

Now, we can solve for \( Y_b \) (the year of birth) in terms of \( Y_c \) (the current year):

\[
Y_b = \frac{2Y_c - 120}{3}
\]

Once we know the current year \( Y_c \), we can calculate \( Y_b \) and then determine her age.

If you let me know the current year (e.g., 2024), I can solve this completely for her exact birth year and age.

Would you like to proceed with that? Let me know!

### Related questions:
1. How does age relate to the difference between two years?
2. What is the importance of simplifying equations in solving word problems?
3. Can you describe how to set up an equation for age-based problems?
4. How would this problem change if Ms. Willow gave a different result instead of 60?
5. What steps would you take if you wanted to generalize this problem for any age?

### Tip:
When tackling word problems, always try to translate the problem into a mathematical equation first before attempting to solve it. This makes the relationships between variables clearer!

At her birthday party, Ms. Willow would not give her age directly. She said, 'If you add the year of my birth to this year, subtract the year of my 15th birthday and the year of my 45th birthday, and then add my present age, the result is 60.'

Learn how to solve Ms. Willow's age problem using algebraic equations. This problem involves linear equations and age-related algebra concepts. Suitable for students in Grades 9-11, this solution provides a step-by-step breakdown of how to find Ms. Willow's birth year and age.

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