Bao is planning a formal event for his college fraternity. The company he is using to cater the event charges a flat rate to reserve the event space plus an additional charge per person attending the event. What does the company charge to reserve the space and how much do they charge per person?

Question

Cost (in dollars)
2,000-
1,500-
1,000-
500-
(0,250)
(20,610)
0
20
40
People
60

18
250
360
20

Answer 1

To find the charge for reserving the event space and the cost per person, we can analyze the information given. It seems that there is a pattern in the costs based on the number of attendees.

Let’s denote the fixed cost to reserve the space as \( C \), and the cost per person as \( P \). The total cost can be represented with the following equation:

\[ \text{Total Cost} = C + P \times \text{Number of People} \]

From the data points provided, we have:

1. For 20 people, the cost is $1,500.
2. For 40 people, the cost is $2,000.
3. For 60 people, the cost is $2,500.

We can set up a system of equations to find \( C \) and \( P \).

From the first data point, \[ C + 20P = 1500 \quad (1) \]

From the second data point, \[ C + 40P = 2000 \quad (2) \]

From the third data point, \[ C + 60P = 2500 \quad (3) \]

Now we can solve this system. Let's subtract equation (1) from equation (2):

\[ (C + 40P) - (C + 20P) = 2000 - 1500 \]

This simplifies to: \[ 20P = 500 \implies P = 25 \]

Now substituting \( P = 25 \) back into equation (1):

\[ C + 20(25) = 1500 \] \[ C + 500 = 1500 \] \[ C = 1000 \]

So, the charges are as follows:

• The company charges $1,000 to reserve the event space.
• They charge $25 per person attending the event.

Thus, the final answer is:

• Reserve Space Charge: $1,000
• Cost Per Person: $25