gsm8k-0021

# GSM8K Problem 22

Raymond and Samantha are cousins. Raymond was born 6 years before Samantha. Raymond had a son at the age of 23. If Samantha is now 31, how many years ago was Raymond's son born?

Reason step by step, then give ONLY the final answer on the last line as \boxed{ANSWER}.

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The user wants me to solve a word problem involving ages.

**1. Understand the goal:**
The goal is to find out how many years ago Raymond's son was born.

**2. Identify the given information:**
*   Raymond and Samantha are cousins.
*   Raymond was born 6 years before Samantha.
*   Raymond had a son at the age of 23.
*   Samantha is now 31 years old.

**3. Set up the relationships:**
Let $R$ be Raymond's current age.
Let $S$ be Samantha's current age.
Let $B_R$ be the year Raymond was born.
Let $B_S$ be the year Samantha was born.
Let $B_{Son}$ be the year Raymond's son was born.

**4. Translate the statements into equations:**
*   "Raymond was born 6 years before Samantha":
    $R = S + 6$
    (Since Raymond is older, his current age is Samantha's age plus 6).
    Alternatively, $B_R = B_S - 6$.

*   "Samantha is now 31":
    $S = 31$

*   "Raymond had a son at the age of 23":
    $R_{at\_son\_birth} = 23$
    This means the son was born when Raymond was 23.
    So, $B_{Son} = B_R - 23$ (or $R - 23$).

**5. Perform the calculations:**
*   From $S = 31$ and $R = S + 6$:
    $R = 31 + 6 = 37$.
    So, Raymond is currently 37 years old.

*   Raymond had his son when he was 23.
    The age of the son now is $R - 23$.
    Wait, the question asks "how many years ago was Raymond's son born?".
    This is equivalent to finding the age of Raymond's son now? No, "how many years ago" is the time elapsed since the birth.
    If Raymond is 37 now, and he was 23 when the son was born, the time elapsed is $37 - 23$.

    Let's double check.
    Current time $T$.
    Raymond's age at $T$ is 37.
    Son's birth time $T_{birth}$.
    Raymond's age at $T_{birth}$ is 23.
    The number of years ago is $T - T_{birth}$.
    Since Age($T$) - Age($T_{birth}$) = (Time elapsed) * (Rate of aging), and rate is 1 year/year.
    So, Years ago = $37 - 23$.

    Calculation:
    $37 - 23 = 14$.

**6. Verify the steps:**
*   Samantha is 31.
*   Raymond is 6 years older than Samantha.
    Raymond = $31 + 6 = 37$.
*   Raymond had a son at age 23.
    This means the son was born 23 years after Raymond was born.
    Since Raymond is 37 now, the son was born $37 - 23 = 14$ years ago.

**7. Structure the final response:**
*   State Samantha's age.
*   Calculate Raymond's age based on the age difference.
*   Calculate the time elapsed since the son's birth based on Raymond's current age and his age at the time of the son's birth.
*   State the final answer.

**Step-by-step breakdown:**
1.  **Samantha's Age:** We are given that Samantha is currently 31 years old.
2.  **Raymond's Age:** Raymond was born 6 years before Samantha. This means Raymond is 6 years older than Samantha.
    Raymond's Age = Samantha's Age + 6
    Raymond's Age = $31 + 6 = 37$ years old.
3.  **Son's Birth:** Raymond had a son at the age of 23.
    This means the son was born when Raymond was 23.
4.  **Years Ago:** To find out how many years ago the son was born, we subtract Raymond's age at the time of the son's birth from his current age.
    Years Ago = Raymond's Current Age - Raymond's Age at Son's Birth
    Years Ago = $37 - 23$
    Years Ago = 14.

The logic holds up.

**Final Answer:** 14.

Let's double check if there are any trick interpretations.
"Raymond was born 6 years before Samantha." -> Raymond is older. Correct.
"Raymond had a son at the age of 23." -> Son born when Raymond is 23. Correct.
"Samantha is now 31." -> Current time reference. Correct.
"How many years ago was Raymond's son born?" -> Current time - Son's birth time. Correct.

Calculation: $31 + 6 = 37$. $37 - 23 = 14$.

Seems straightforward.

One potential pitfall: "Raymond was born 6 years before Samantha".
Does this mean Raymond is 6 years older? Yes.
Example: Raymond born 2000, Samantha born 2006. Raymond is 6 years older.
If Samantha is 31 (born 1993? No, $2024-31 = 1993$).
If Samantha is 31, Raymond is $31+6 = 37$.
Raymond born $2024-37 = 1987$.
Samantha born $2024-31 = 1993$.
Difference: $1993 - 1987 = 6$. Correct