Your task:
1. Let \( n \) represent the number in step 1 and show what happens through step 6.
- **Step 1**: Pick a number \( n \).
- **Step 2**: Double it. Result: \( 2n \).
- **Step 3**: Add 5. Result: \( 2n + 5 \).
- **Step 4**: Multiply by 50. Result: \( 50(2n + 5) = 100n + 250 \).
- **Step 5**: If you've had your birthday this year, add 1764; if not, add 1763.
- Result if birthday has passed: \( 100n + 250 + 1764 = 100n + 2014 \).
- Result if birthday has not passed: \( 100n + 250 + 1763 = 100n + 2013 \).
- **Step 6**: Subtract the year of your birth.
2. Explain why the result is always the original number followed by your age.
- After step 6, the number becomes \( 100n + (current \ year - birth \ year) \).
- The expression \( current \ year - birth \ year \) gives your age, so the result is \( 100n \) (which shows the original number) followed by your age.
Answer (2)
if I pick n, it becomes 50(2n+5)+1764-2001 this is the expression
The process begins with picking a number n , and through a series of operations, you end up with a number that concatenates your original number and your age. This happens because the calculations isolate your age based on the current year minus your birth year. Therefore, the final result reveals your original number along with your age.
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