On itv's homework hotline, it's time for "rudolf's rules." if you guess what rule rudolf is using you get a prize. someone puts golf balls into a miniature-golf display called rudolf, then rudolf sends back a certain number of golf balls. today rudolf gets 8 balls and sends back 6. next rudolf gets 15 and sends back 27. when he gets 25, 57 are returned. if n represents the number of balls initially given to rudolf, write an expression to represent how many balls he sent back.

y = 3x -18 ( where y =  balls sent back by Rudolf; x= balls  given to Rudolf)

Step-by-step explanation:

x (Balls given)       y( Balls sent back)

8                             6                    Δy/Δx  = (27-6)/(15-8) =  3

15                            27

25                           57                 Δy/Δx  = (57-27)/(25-15) =  3

Observing the number sequence shows constant gradient and as such we can use equation of a straight line to relate the two variables.

Using the equation of a straight line we have:

(y-y1)/(x-x1) =  (y2-y1)/(x2-x1)

y-6/x-8  =       (27-6)/(15-8)

y-6/x-8  =    3

y-6        =  3(x-8)

y-6  = 3x - 24

y = 3x-18

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.