On ITV\'s Homework Hotline, it\'s time for \"Rudolf\'s Rules.\" If you guess wha

Question

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. First, solve whatever way you would normally use. Then, try to write a number sentence, using the Order of Operations.

Explanation / Answer

We can observe that Rudolf always returns the number of balls in multiples of 3.

So f(n) = 3(n - a)

For n = 8, f(n) = 6

6 = 3(8 - a)

=> a = 6

Hence f(n) = 3(n - 6)

Similarly, for n = 25,

f(25) = 3(25 - 6)

= 3(19)

57

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