What is the conjecture that release the result of the process to the original number selected?

Question

Repeat the following procedure for the four given numbers.

Multiply the number by 6. Add 10 to the product. Divide this sum by 2. Subtract 5 from the quotient.

The 1st number is

1.

The result is

3.

The 2nd number is

5.

The result is

1 5.

The 3rd number is

9.

The result is

27.

The 4th number is

11.

The result is

33.

Write a conjecture that relates the result of the process to the original number selected. Represent the original number as n. The result is

Answer 1

6N + 10

---------- - 5 =

2

3N + 5 - 5

3N

so yes, you will always get triple the original number. or 3N.

A final step should be to divide the last difference by 3, which gets you

the original number back.