Question

The cost (y) per person of renting out a conference room varies inversely with the number of people (x) in attendance. It costs $30 per person if 100 people attend.

1. Find the constant of variation:
2.Write an equation that relates the variables:
3.How much would it cost if 240 people attended?

Answer 1

Inverse variation:

Answer 2

\[y=\frac{k}{x}\]

Answer 3

Replace y with 30 and x with 100 and find the constant k

Answer 4

So 30 = k100?

Answer 5

k/100

Answer 6

yes. k/100

Answer 7

Wouldn't that simply be 3000?

Answer 8

Yes. k=3000 so now the equation is:

Answer 9

\[y=\frac{3000}{x}\]

Answer 10

Now replace x with 240 and find y

Answer 11

12.5?

Answer 12

Yes. It would cost $12.50 person if 240 people attended.

Answer 13

Thanks so much. To clarify:
1. k=3000
2. Y=3000/X
3. Y=$12.50
Correct?

Answer 14

Yes. And that makes sense because if you serve more people, the cost per person should go down.

Answer 15

Okay thanks so much again . :)

Answer 16

yw