Please Help ME With This

Question

 $300 base price plus $20 per guest for up to 30 guests

Complete the following tasks

1. Write an equation where x is the number of guests and y is the total cost of the party.
2. Are their any values x cannot equal? If so, why?
3. What would be the cost of the party if Madelyn invites 28 people?

Answer 1

1) Let x = number of guests

Total Cost, C(x) = 20x + 300 ; 0< x ≤30

2) x cannot be zero or you would be charged $300 for nothing

3) C(30) = 20(28)+ 300 = $860

Answer 2

1) y = 300 + 20x

2) we are told that the number of guests is limited to 30 or less so x cannot be greater than 30. Of course, it also must be greater than or equal to zero as well.

3) y = 300 + 20(28)

y = 300 + 560

y = 860

So the cost is $860 for 28 people

Answer 3

1. since you are told to let y = the total cost and the total cost will include the base price PLUS the cost for each guest (20 PER guest, so 20x); y = 20x + 300
2. if x represents the number of PEOPLE then it wouldn't make sense if x was negative. In addition, the problem states "up to 30 guests" so x cannot be more than 30. Finally....back to x representing PEOPLE....x can't be a fraction or decimal. Therefore, x must be a whole number greater or equation to 0 and less than or equal to 30.
3. 28 represents the number of guests attending...which is represented by x. Therefore, we substitute 28 for x in the equation we wrote in #1. y = 20(28) + 300

:-)