Question
1)) Write a system of equations to describe the situation below, solve using any method, and
fill in the blanks.
()) A charity is considering the possibility of having a benefit night at two different
restaurants. The owner of the local Italian restaurant has offered to make a donation of
and
he could contribute
promised to participate in the event; it appears that each restaurant would donate the same
total amount. How many diners promised to participate? How much would each restaurant
donate?
()) With
fill in the blanks.
()) A charity is considering the possibility of having a benefit night at two different
restaurants. The owner of the local Italian restaurant has offered to make a donation of
and
he could contribute
promised to participate in the event; it appears that each restaurant would donate the same
total amount. How many diners promised to participate? How much would each restaurant
donate?
()) With
Ask by Haynes Medina. in the United States
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
14 diners promised to participate, and each restaurant would donate $248.
Solution
Let
The donations are given by:
- Italian restaurant:
- Mexican restaurant:
Since both restaurants donate the same total amount, we set:
Step 1: Solve for
Subtract
Subtract
Divide both sides by 2:
Step 2: Find the donation amount
Substitute
For verification, using the Mexican restaurant’s equation:
Answer:
- Number of diners promised to participate:
- Each restaurant would donate:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Explain 
Simplify this solution Mind Expander
Let
For the Mexican restaurant, with
Since the problem states that both donations are equal, we set up the equation:
To satisfy the condition, we know the number of diners promised at both restaurants will be equal, so
Now we can rewrite our equation:
This simplifies to:
Thus, there are 14 diners promised to participate at each restaurant.
Now, substituting
Italian restaurant donation:
Mexican restaurant donation:
To summarize, 14 diners promised to participate, and each restaurant would donate
The concept of benefit nights has a charming history steeped in community spirit! The first fundraisers typically took place in the 19th century, where gatherings at local establishments created a sense of camaraderie while raising funds for local causes—talk about dining for a cause!
When planning your own benefit night, it’s essential to budget wisely and understand the expected number of participants. A common mistake is underestimating the expenses that could arise from hosting an event, such as venue costs and promotional materials. Planning carefully helps ensure that the event is profitable for your charity!
