rlene plants turnip plants for a greenhouse. She is paid $12.50 per hour, plus $2.76 for each turnip plant planted in excess of 24, in a 7.50-hour daily shift. Irlene typically plants 10 turnip plants per hour.

a) What would typically be Irlene's daily piecework earnings? For full marks your answer(s) should be rounded to the nearest cent.

Piecework earnings = $0.00 

b) What would typically be Irlene's total daily earnings? For full marks your answer(s) should be rounded to the nearest cent.

Daily earnings = $0.00 


To determine Irlene's piecework and total daily earnings, we need to break down her earnings from both her hourly wage and her piecework. Let's go through each part step by step:

### Part (a): Daily Piecework Earnings

1. **Calculate the total number of turnip plants planted per day:**

   Irlene plants 10 turnip plants per hour, and she works for 7.5 hours per day.
   
   \[
   \text{Total Turnip Plants} = 10 \text{ plants/hour} \times 7.5 \text{ hours} = 75 \text{ plants}
   \]

2. **Determine the number of turnip plants in excess of 24:**

   \[
   \text{Excess Turnip Plants} = 75 \text{ plants} - 24 \text{ plants} = 51 \text{ plants}
   \]

3. **Calculate the piecework earnings:**

   Irlene is paid $2.76 for each turnip plant planted in excess of 24.
   
   \[
   \text{Piecework Earnings} = 51 \text{ plants} \times \$2.76/\text{plant} = 51 \times 2.76 = \$140.76
   \]

### Part (b): Total Daily Earnings

1. **Calculate the daily earnings from the hourly wage:**

   Irlene is paid $12.50 per hour and works 7.5 hours per day.
   
   \[
   \text{Hourly Wage Earnings} = 7.5 \text{ hours} \times \$12.50/\text{hour} = 7.5 \times 12.50 = \$93.75
   \]

2. **Calculate the total daily earnings by adding the piecework earnings to the hourly wage earnings:**

   \[
   \text{Total Daily Earnings} = \text{Hourly Wage Earnings} + \text{Piecework Earnings}
   \]
   
   \[
   \text{Total Daily Earnings} = \$93.75 + \$140.76 = \$234.51
   \]

Therefore:

a) Irlene's daily piecework earnings = $140.76

b) Irlene's total daily earnings = $234.51

Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. How much would Irlene earn in a week if she worked 5 days under the same conditions?
2. If Irlene planted 15 turnip plants per hour, what would be her daily piecework earnings?
3. How would Irlene's earnings change if she worked an 8-hour shift instead of 7.5 hours?
4. What is the minimum number of turnip plants Irlene needs to plant to earn more from piecework than from her hourly wage in a day?
5. If the payment per excess turnip plant increased to $3.00, how would her piecework earnings change?
6. What is Irlene's hourly rate of earning if both her hourly wage and piecework earnings are considered?
7. How many turnip plants must Irlene plant to earn at least $300 in a day?
8. If Irlene's hourly wage was reduced to $10.00 per hour, how would her total daily earnings be affected?

**Tip:** When calculating earnings that combine a fixed hourly wage and a variable piecework component, it is important to separately account for each part and then sum them for the total. This approach ensures accurate and comprehensive calculations.

Learn how to calculate Irlene's daily piecework and total earnings based on her hourly wage and the number of turnip plants planted. This problem involves understanding piecewise functions and calculating earnings with a combination of fixed and variable rates. Suitable for advanced high school students.

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