Final answer:
The maximum number of people that can attend the reception while keeping the cost under $45,000 is 77, which is closest to answer choice (A) 75. However, this does not exactly match the provided answer choices, indicating a possible error in the question's details. To provide a context example, the total cost of a dinner with an 18% tip on a $72 bill was calculated to be $84.96.
Step-by-step explanation:
To determine how many people can attend the reception while keeping the cost below $45,000, we can use the equation for the total cost, which is the sum of the flat fee and the cost per person multiplied by the number of people.
Let x be the number of people that can attend. The equation for the total cost is:
10,000 + 450x < 45,000
Subtract 10,000 from both sides to find the amount available for the dinner per person:
450x < 35,000
Divide both sides by 450 to solve for x:
x < 77.78
Since we can't have a fraction of a person attending, the largest whole number of people that can attend is 77. However, this does not match any of the answer choices provided (A) 75, (B) 80, (C) 85, (D) 90. The closest option without going over is (A) 75.
It seems there may be a typo in the question or the answer choices, as none of the answer choices match the calculated number.
Now, let's address the unrelated example of the family dinner. To calculate the total cost of the dinner with tip:
Total meal cost = $72
Tip = 18% of $72
Tip = 0.18 * $72
Tip = $12.96
Total cost with tip = Meal cost + Tip
Total cost with tip = $72 + $12.96
Total cost with tip = $84.96