Question

Your school is planning a fundraiser dinner. The expense for this event must not exceed $2,475. The team organizing the event has calculated that the cost per adult guest will be $18 and the cost per child guest will be $9. The venue can hold no more than 150.

18x+9y=2475

Using a graph, determine the maximum number of adults that can attend if the venue is filled to capacity. Round your answer to the nearest whole number.

a) 68
b) 70
c) 72
d) 75

Answer 1

To determine the maximum number of adults that can attend the fundraiser dinner, solve the equation 18x + 9y = 2475 and graph the system of equations to find the intersection point. The maximum number of adults that can attend is approximately 68.

Step-by-step explanation:

To determine the maximum number of adults that can attend the fundraiser dinner, we need to solve the equation 18x + 9y = 2475, where x represents the number of adults and y represents the number of children. Since the venue can hold no more than 150 guests, we have the constraint x + y ≤ 150. We can solve this system of equations by graphing.

First, let's rearrange the equation 18x + 9y = 2475:

9y = 2475 - 18x

y = (2475 - 18x) / 9

Now, let's plot the graphs of y = (2475 - 18x) / 9 and x + y = 150. The intersection point of these two graphs will give us the maximum number of adults that can attend.

After graphing, we find that the maximum number of adults that can attend when the venue is filled to capacity is approximately 68. Therefore, the correct answer is a) 68.