please help!!! We can't get it

Question

Clara and her friends are planning a trip to paintball park. Find the cost of lunch and the cost of each paintball. What would the cost be for 400 paint balls and lunch?          •$25 for 500 Paintballs 

                   •$15 for 200 Paintballs

Answer 1

Hi Sarah,

 

Let's assume that the cost of lunch is included and the relationship is linear

 

then we have two points

 

15,200   and 25,500

 

find the rate of change in price (slope)

 

(y-y)/(x-x)

 

(500-200)/(25-15)

 

300/10

 

30

 

so

 

y = 30x + b   (where y equals total number of paintballs and x equal cost in dollars

 

200 = 30(15) + b

 

b = -250

 

our equation would be

 

y = 30x - 250

 

and to find the value of x when y = 400 we substitue and solve

 

400 = 30x - 250

 

650 = 30x

 

x = 21.66   (so it costs 21.66 to get lunch and 400 paintballs

 

each additional paint ball would be 30 for $1 dollar or 3.33 cents per paintball

 

Hope this helps