Question

Darren's birthday party will cost $40 if he invites 5 guests. If there are 6 guests, how muchwill Darren's birthday party cost? Assume the relationship is directly proportional.

Answer 1

Let y be the cost of the party and x the number of guests. Since we are told to assume that the relationship is directlly proportional, we have that

$y=kx$

where k is a positive constant.

We are told that y is 40 whenever x is 5. So we have the equation

$40=k\cdot5$

so, multiplying both sides by 5, we get

$k=\frac{40}{5}=8$

So we have the equation

$y=8x$

Now, we are interested in finding y when x=6. So we have that

$y=8\cdot6=48$

So the cost for a party of 6 is 48.