Question

The amount of fun P. Art Eman has at a party is inversely proportional to the number of people at the party. So, if he is having twice as much fun at a birthday party as he had at last week's holiday party, what is the relationship in the number of people at the two parties?
a. Twice as many at the second party
b. Four times as many at the second party
c. Half as many at the second party
d. The numbers are the same.

Answer 1

Answer:

There are half as many at the birthday party.

Step-by-step explanation:

The amount of fun that Eman has at a party is inversely proportional to the number of people at the party.

If F represents the amount of fun and N represents the number of people in the party, then F ∝ 1/ N

So, comparing last week's holiday party where fun was $F_{h}$ and number of people was $N_{h}$ and the birthday party where fun is $F_{b}$ and the number of people is $N_{b}$, we can write

$F_{h}N_{h} = F_{b}N_{b}$

⇒ $N_{b} = \frac{F_{h} }{F_{b}} \times N_{h} = \frac{N_{h}}{2}$

{Since, Eman is having twice as much fun at a birthday party as he had at last week's holiday party}

Therefore, there are half as many people at the birthday party. (Answer)