gsm8k-0009

# GSM8K Problem 10

Eliza's rate per hour for the first 40 hours she works each week is $10. She also receives an overtime pay of 1.2 times her regular hourly rate. If Eliza worked for 45 hours this week, how much are her earnings for this week?

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 about calculating earnings based on regular and overtime hours.

**1. Understand the problem:**
*   **Regular rate:** $10 per hour.
*   **Regular hours limit:** 40 hours per week.
*   **Overtime rate:** 1.2 times the regular hourly rate.
*   **Total hours worked:** 45 hours.
*   **Goal:** Calculate total earnings for the week.

**2. Break down the calculation:**
*   **Step 1: Calculate regular earnings.**
    *   Eliza works 40 regular hours.
    *   Rate = $10/hour.
    *   Regular earnings = $40 \times 10$.

*   **Step 2: Calculate overtime hours.**
    *   Total hours = 45.
    *   Regular hours = 40.
    *   Overtime hours = Total hours - Regular hours = $45 - 40$.

*   **Step 3: Calculate overtime rate.**
    *   Regular rate = $10.
    *   Overtime multiplier = 1.2.
    *   Overtime rate = $10 \times 1.2$.

*   **Step 4: Calculate overtime earnings.**
    *   Overtime earnings = Overtime hours $\times$ Overtime rate.

*   **Step 5: Calculate total earnings.**
    *   Total earnings = Regular earnings + Overtime earnings.

**3. Execute the calculation:**
*   **Regular earnings:** $40 \times 10 = 400$.
*   **Overtime hours:** $45 - 40 = 5$.
*   **Overtime rate:** $10 \times 1.2 = 12$.
*   **Overtime earnings:** $5 \times 12 = 60$.
*   **Total earnings:** $400 + 60 = 460$.

**4. Verify the steps:**
*   Did I interpret "1.2 times her regular hourly rate" correctly? Yes, usually overtime is calculated as a percentage increase or a multiplier. 1.2 times means 20% more.
*   Did I identify the cutoff correctly? "first 40 hours". Yes.
*   Did I subtract correctly? $45 - 40 = 5$.
*   Did I multiply correctly? $40 \times 10 = 400$, $5 \times 12 = 60$, $400 + 60 = 460$.

**5. Formulate the final response:**
*   State the regular pay calculation.
*   State the overtime hours calculation.
*   State the overtime rate calculation.
*   State the overtime pay calculation.
*   Sum them up.
*   Provide the boxed answer.

**Step-by-step derivation:**
1.  **Regular Pay:** Eliza works 40 hours at the regular rate of $10/hour.
    $$40 \text{ hours} \times \$10/\text{hour} = \$400$$
2.  **Overtime Hours:** She worked a total of 45 hours. The hours over 40 are overtime.
    $$45 \text{ hours} - 40 \text{ hours} = 5 \text{ overtime hours}$$
3.  **Overtime Rate:** The overtime rate is 1.2 times the regular rate.
    $$1.2 \times \$10/\text{hour} = \$12/\text{hour}$$
4.  **Overtime Pay:**
    $$5 \text{ hours} \times \$12/\text{hour} = \$60$$
5.  **Total Earnings:**
    $$\$400 \text{ (regular)} + \$60 \text{ (overtime)} = \$460$$

The final answer is 460.

Double check the wording: "Eliza's rate per hour for the first 40 hours she works each week is $10." -> Regular pay is $10/hr for first 40 hours.
"She also receives an overtime pay of 1.2 times her regular hourly rate." -> Overtime rate is $10 * 1.2 = $12/hr.
"If Eliza worked for 45 hours this week" -> 40 regular + 5 overtime.
Calculation: $(40 * 10) + (5 * 12) = 400 + 60 = 460$.

Looks solid.

One potential ambiguity: Does "overtime pay of 1.2 times her regular hourly rate" mean the *total* pay for that hour is 1.2x, or is it an *additional* 1.2x (i.e., 2.2x)?
Standard interpretation in math problems (and employment law usually) is that the rate *is* 1.2 times the regular rate. If it meant "an additional 1.2 times", it would usually say "an additional 1.2 times" or "120% increase". "Overtime pay of X" usually defines the rate for that time.
Let's stick to the standard interpretation: Rate = $10 * 1.2 = $12.

If it were an increase of 1.2 times (meaning 220% of regular), the math would be:
$400 + (5 * 10 * 2.2) = 400 + 110 = 510$.
However, "overtime pay of 1.2 times her regular hourly rate" is a definition of the rate. "I get paid 1.2 times my normal rate". This means Rate = 1.2 * Normal.
So $12/hr is the correct interpretation.

Final check.
Regular: 40 * 10 = 400.
Overtime: 5 hours.
Rate: 10 * 1.2 = 12.
Overtime Pay: 5 * 12 = 60.
Total: 460.

The quest