Answer:
Explanation:
To create a word model, equation, and solve the problem of how many hours it will take to make all eight dozen cookies, follow these steps:
**Step 1: Define Variables**
- Let M represent the number of minutes needed to mix and bake each batch.
- Let B represent the number of batches.
**Step 2: Set Up the Word Model**
- In the first two batches, you spend 30 minutes on each batch, so you have 2 batches * 30 minutes/batch = 60 minutes for those batches.
- For the remaining batches (batch 3 and onwards), you spend 20 minutes on each batch.
So, the total time T in minutes for all B batches can be represented as follows:
**T = 60 (minutes) + (B - 2) * 20 (minutes)**
**Step 3: Convert to Hours**
- Since there are 60 minutes in an hour, you need to convert the total time T from minutes to hours. Divide T by 60:
**T (hours) = [60 + (B - 2) * 20] / 60**
**Step 4: Solve for B**
- You want to make a total of 8 dozen (8 x 12) cookies, which is 96 cookies. Each batch makes one dozen (12) cookies.
So, set up an equation for the number of batches needed to make 96 cookies:
**B * 12 = 96**
Now, solve for B:
**B = 96 / 12 = 8 batches**
**Step 5: Substitute B into the Time Equation**
- Now that you know you need 8 batches, substitute this value into the time equation:
T (hours) = [60 + (8 - 2) * 20] / 60
**Step 6: Calculate the Total Time in Hours**
- Simplify and calculate the total time T in hours:
T (hours) = [60 + 6 * 20] / 60
T (hours) = [60 + 120] / 60
T (hours) = 180 / 60
T (hours) = 3 hours
So, it will take you a total of 3 hours to make all eight dozen cookies for the bake sale.