Calculate the gross pay of Alice, a corn picker, assuming she picked 4,150 ears of corn:

**Note: Round your final answer to the nearest cent.**

Corn PickedRate per ear

1 − 2,000

$ 0.04 per ear

2,001 − 3,000

0.05 per ear

Over 3,000

0.09 per ear


To calculate Alice's gross pay based on the number of ears of corn she picked and the corresponding rates, we need to break down the total into the relevant segments and then calculate the pay for each segment.

### Step 1: Calculate the pay for the first 2,000 ears
\[ \text{Pay for first 2,000 ears} = 2,000 \times 0.04 = 80.00 \]

### Step 2: Calculate the pay for the next 1,000 ears (2,001 to 3,000)
\[ \text{Pay for next 1,000 ears} = 1,000 \times 0.05 = 50.00 \]

### Step 3: Calculate the pay for the remaining ears over 3,000
Alice picked a total of 4,150 ears. The number of ears over 3,000 is:
\[ \text{Ears over 3,000} = 4,150 - 3,000 = 1,150 \]

\[ \text{Pay for 1,150 ears over 3,000} = 1,150 \times 0.09 = 103.50 \]

### Step 4: Calculate the total gross pay
Now, add up the pay for each segment:
\[ \text{Total Gross Pay} = 80.00 + 50.00 + 103.50 = 233.50 \]

So, Alice's gross pay is **$233.50**.

Would you like more details or have any questions?

Here are five questions you might consider next:
1. How do tiered pay structures work in different industries?
2. What are the advantages and disadvantages of piece-rate pay?
3. How can Alice increase her efficiency to maximize earnings?
4. How do labor laws affect piece-rate workers?
5. What are some common methods for tracking and verifying piece-rate work?

**Tip:** Always ensure you correctly identify and apply each rate segment when calculating piece-rate pay, especially when dealing with varying rates for different quantities.

Learn how to calculate Alice's gross pay based on the number of ears of corn picked using a piecewise function. This problem involves different rates per ear for specified ranges, demonstrating practical application of piecewise functions in mathematics. Suitable for Grades 7-9.

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