Question
Addison learned a total of 25 appetizer recipes over the course of 5 weeks of culinary school. After how many weeks of culinary school will Addison know a total of 40 appetizer recipes? Solve using unit rates.
Answers
GPT-4o mini
To solve this problem using unit rates, we first need to determine how many appetizer recipes Addison learned per week.
**Step 1: Calculate the rate of recipes learned per week.**
Addison learned 25 appetizer recipes over 5 weeks. We can calculate the unit rate as follows:
\[
\text{Rate} = \frac{\text{Total recipes}}{\text{Total weeks}} = \frac{25 \text{ recipes}}{5 \text{ weeks}} = 5 \text{ recipes per week}
\]
**Step 2: Determine how many additional recipes are needed to reach 40 recipes.**
We want to find out how many more recipes Addison needs to learn to reach a total of 40 appetizer recipes:
\[
\text{Additional recipes needed} = 40 \text{ recipes} - 25 \text{ recipes} = 15 \text{ recipes}
\]
**Step 3: Calculate the number of weeks required to learn the additional recipes.**
Using the unit rate calculated earlier (5 recipes per week), we can find out how many weeks it will take to learn the additional 15 recipes:
\[
\text{Weeks needed} = \frac{\text{Additional recipes needed}}{\text{Rate}} = \frac{15 \text{ recipes}}{5 \text{ recipes per week}} = 3 \text{ weeks}
\]
**Step 4: Calculate the total weeks of culinary school.**
Add to the initial 5 weeks:
\[
\text{Total weeks} = 5 \text{ weeks} + 3 \text{ weeks} = 8 \text{ weeks}
\]
Thus, Addison will know a total of 40 appetizer recipes after **8 weeks** of culinary school.
**Step 1: Calculate the rate of recipes learned per week.**
Addison learned 25 appetizer recipes over 5 weeks. We can calculate the unit rate as follows:
\[
\text{Rate} = \frac{\text{Total recipes}}{\text{Total weeks}} = \frac{25 \text{ recipes}}{5 \text{ weeks}} = 5 \text{ recipes per week}
\]
**Step 2: Determine how many additional recipes are needed to reach 40 recipes.**
We want to find out how many more recipes Addison needs to learn to reach a total of 40 appetizer recipes:
\[
\text{Additional recipes needed} = 40 \text{ recipes} - 25 \text{ recipes} = 15 \text{ recipes}
\]
**Step 3: Calculate the number of weeks required to learn the additional recipes.**
Using the unit rate calculated earlier (5 recipes per week), we can find out how many weeks it will take to learn the additional 15 recipes:
\[
\text{Weeks needed} = \frac{\text{Additional recipes needed}}{\text{Rate}} = \frac{15 \text{ recipes}}{5 \text{ recipes per week}} = 3 \text{ weeks}
\]
**Step 4: Calculate the total weeks of culinary school.**
Add to the initial 5 weeks:
\[
\text{Total weeks} = 5 \text{ weeks} + 3 \text{ weeks} = 8 \text{ weeks}
\]
Thus, Addison will know a total of 40 appetizer recipes after **8 weeks** of culinary school.
Gregoriah
Edgar took a total of 40 pages of notes during 8 hours of class. In all, how many hours will Edgar have to spend in class before he will have a total of 70 pages of notes in his notebook? Solve using unit rates.
GPT-4o mini
To solve this problem using unit rates, we first need to determine how many pages of notes Edgar takes per hour.
**Step 1: Calculate the rate of pages taken per hour.**
Edgar took 40 pages of notes in 8 hours. We can calculate the unit rate as follows:
\[
\text{Rate} = \frac{\text{Total pages}}{\text{Total hours}} = \frac{40 \text{ pages}}{8 \text{ hours}} = 5 \text{ pages per hour}
\]
**Step 2: Determine how many additional pages are needed to reach 70 pages.**
To find out how many more pages Edgar needs to take to reach a total of 70 pages:
\[
\text{Additional pages needed} = 70 \text{ pages} - 40 \text{ pages} = 30 \text{ pages}
\]
**Step 3: Calculate the number of hours required to take the additional pages.**
Using the unit rate we calculated earlier (5 pages per hour), we find out how many hours it will take to take the additional 30 pages:
\[
\text{Hours needed} = \frac{\text{Additional pages needed}}{\text{Rate}} = \frac{30 \text{ pages}}{5 \text{ pages per hour}} = 6 \text{ hours}
\]
**Step 4: Calculate the total hours of class.**
Add this to the initial 8 hours:
\[
\text{Total hours} = 8 \text{ hours} + 6 \text{ hours} = 14 \text{ hours}
\]
Thus, Edgar will have to spend a total of **14 hours** in class before he will have a total of 70 pages of notes in his notebook.
**Step 1: Calculate the rate of pages taken per hour.**
Edgar took 40 pages of notes in 8 hours. We can calculate the unit rate as follows:
\[
\text{Rate} = \frac{\text{Total pages}}{\text{Total hours}} = \frac{40 \text{ pages}}{8 \text{ hours}} = 5 \text{ pages per hour}
\]
**Step 2: Determine how many additional pages are needed to reach 70 pages.**
To find out how many more pages Edgar needs to take to reach a total of 70 pages:
\[
\text{Additional pages needed} = 70 \text{ pages} - 40 \text{ pages} = 30 \text{ pages}
\]
**Step 3: Calculate the number of hours required to take the additional pages.**
Using the unit rate we calculated earlier (5 pages per hour), we find out how many hours it will take to take the additional 30 pages:
\[
\text{Hours needed} = \frac{\text{Additional pages needed}}{\text{Rate}} = \frac{30 \text{ pages}}{5 \text{ pages per hour}} = 6 \text{ hours}
\]
**Step 4: Calculate the total hours of class.**
Add this to the initial 8 hours:
\[
\text{Total hours} = 8 \text{ hours} + 6 \text{ hours} = 14 \text{ hours}
\]
Thus, Edgar will have to spend a total of **14 hours** in class before he will have a total of 70 pages of notes in his notebook.
Gregoriah
Mackenzie's office recycled a total of 20 kilograms of paper over 5 weeks. After 6 weeks, how many kilograms of paper will Mackenzie's office have recycled? Solve using unit rates.
GPT-4o mini
To solve this problem using unit rates, we first need to find out how many kilograms of paper Mackenzie's office recycles per week.
**Step 1: Calculate the rate of recycling per week.**
Mackenzie's office recycled 20 kilograms of paper over 5 weeks. We can calculate the unit rate as follows:
\[
\text{Rate} = \frac{\text{Total kilograms}}{\text{Total weeks}} = \frac{20 \text{ kg}}{5 \text{ weeks}} = 4 \text{ kg per week}
\]
**Step 2: Calculate the total amount of recycling after 6 weeks.**
Now, we can use this rate to determine how many kilograms of paper will have been recycled after 6 weeks:
\[
\text{Total kilograms after 6 weeks} = \text{Rate} \times \text{Total weeks} = 4 \text{ kg per week} \times 6 \text{ weeks} = 24 \text{ kg}
\]
Thus, after 6 weeks, Mackenzie's office will have recycled a total of **24 kilograms** of paper.
**Step 1: Calculate the rate of recycling per week.**
Mackenzie's office recycled 20 kilograms of paper over 5 weeks. We can calculate the unit rate as follows:
\[
\text{Rate} = \frac{\text{Total kilograms}}{\text{Total weeks}} = \frac{20 \text{ kg}}{5 \text{ weeks}} = 4 \text{ kg per week}
\]
**Step 2: Calculate the total amount of recycling after 6 weeks.**
Now, we can use this rate to determine how many kilograms of paper will have been recycled after 6 weeks:
\[
\text{Total kilograms after 6 weeks} = \text{Rate} \times \text{Total weeks} = 4 \text{ kg per week} \times 6 \text{ weeks} = 24 \text{ kg}
\]
Thus, after 6 weeks, Mackenzie's office will have recycled a total of **24 kilograms** of paper.
Gregoriah
Susan's birthday party will cost $42 if she invites 21 guests. If there are 25 guests, how much will Susan's birthday party cost? Solve using unit rates.
GPT-4o mini
To find out how much Susan's birthday party will cost with 25 guests using unit rates, we first need to determine the cost per guest.
**Step 1: Calculate the cost per guest.**
Susan's birthday party costs $42 for 21 guests. We can calculate the cost per guest as follows:
\[
\text{Cost per guest} = \frac{\text{Total cost}}{\text{Number of guests}} = \frac{42 \text{ dollars}}{21 \text{ guests}} = 2 \text{ dollars per guest}
\]
**Step 2: Calculate the cost for 25 guests.**
Now that we know the cost per guest, we need to find out how much it will cost for 25 guests:
\[
\text{Total cost for 25 guests} = \text{Cost per guest} \times \text{Number of guests} = 2 \text{ dollars per guest} \times 25 \text{ guests} = 50 \text{ dollars}
\]
Thus, if there are 25 guests, Susan's birthday party will cost **$50**.
**Step 1: Calculate the cost per guest.**
Susan's birthday party costs $42 for 21 guests. We can calculate the cost per guest as follows:
\[
\text{Cost per guest} = \frac{\text{Total cost}}{\text{Number of guests}} = \frac{42 \text{ dollars}}{21 \text{ guests}} = 2 \text{ dollars per guest}
\]
**Step 2: Calculate the cost for 25 guests.**
Now that we know the cost per guest, we need to find out how much it will cost for 25 guests:
\[
\text{Total cost for 25 guests} = \text{Cost per guest} \times \text{Number of guests} = 2 \text{ dollars per guest} \times 25 \text{ guests} = 50 \text{ dollars}
\]
Thus, if there are 25 guests, Susan's birthday party will cost **$50**.
Gregoriah
The corporate team-building event will cost $63 if it has 7 attendees. If there are 11 attendees, how much will the corporate team-building event cost? Solve using unit rates.
GPT-4o mini
To determine the cost of the corporate team-building event with 11 attendees using unit rates, we first need to calculate the cost per attendee.
**Step 1: Calculate the cost per attendee.**
The total cost of the event for 7 attendees is $63. We can calculate the cost per attendee as follows:
\[
\text{Cost per attendee} = \frac{\text{Total cost}}{\text{Number of attendees}} = \frac{63 \text{ dollars}}{7 \text{ attendees}} = 9 \text{ dollars per attendee}
\]
**Step 2: Calculate the total cost for 11 attendees.**
Now that we know the cost per attendee, we can find the total cost for 11 attendees:
\[
\text{Total cost for 11 attendees} = \text{Cost per attendee} \times \text{Number of attendees} = 9 \text{ dollars per attendee} \times 11 \text{ attendees} = 99 \text{ dollars}
\]
Thus, if there are 11 attendees, the corporate team-building event will cost **$99**.
**Step 1: Calculate the cost per attendee.**
The total cost of the event for 7 attendees is $63. We can calculate the cost per attendee as follows:
\[
\text{Cost per attendee} = \frac{\text{Total cost}}{\text{Number of attendees}} = \frac{63 \text{ dollars}}{7 \text{ attendees}} = 9 \text{ dollars per attendee}
\]
**Step 2: Calculate the total cost for 11 attendees.**
Now that we know the cost per attendee, we can find the total cost for 11 attendees:
\[
\text{Total cost for 11 attendees} = \text{Cost per attendee} \times \text{Number of attendees} = 9 \text{ dollars per attendee} \times 11 \text{ attendees} = 99 \text{ dollars}
\]
Thus, if there are 11 attendees, the corporate team-building event will cost **$99**.