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.

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.

Answer 6

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.

Answer 7

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.

Answer 8

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.

Answer 9

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.