Answer:
Let's assume that the company invites x people to the dinner party.
The cost of the function room is a fixed cost of $280.
The cost of dinner is $40 per person. Therefore, the total cost of dinner for x people is 40x.
The total cost of the dinner party is the sum of the cost of the function room and the cost of dinner:
Total cost = 280 + 40x
The problem states that the company has a budget of no more than $1500. Therefore, we can write:
280 + 40x ≤ 1500
Subtracting 280 from both sides gives:
40x ≤ 1220
Dividing both sides by 40 gives:
x ≤ 30.5
Since we cannot invite a fraction of a person, the company can invite at most 30 people to the dinner party.
Therefore, the greatest number of people they can invite to the dinner is 30.
Explanation: