Answer to Question #338392 in Discrete Mathematics for Kevin

Question

Consider the following procedure: Pick a number. Multiply the number by 9, add 15 to the product,

divide the sum by 3, and subtract 5. Complete the above procedure for several different numbers. Use

inductive reasoning to make a conjecture about the relationship between the size of the resulting number

and the size of the original number.

Answer 1

Pick a number. Let n=2

Multiply the number by 9. 9(2)=18

Add 15 to the product. 18+15=33

Divide the sum by 3. 33/3=11

Subtract 5. 11-5=6

6/2=3

The size of the resulting number is three times of

the size of the original number.

Pick a number. Let n=1

Multiply the number by 9. 9(1)=9

Add 15 to the product. 9+15=24

Divide the sum by 3. 24/3=8

Subtract 5. 8-5=3

3/1=3

The size of the resulting number is three times of

the size of the original number.

Pick a number. Let n=x

Multiply the number by 9. 9(x)=9x

Add 15 to the product. 9x+15=9x+15

Divide the sum by 3. (9x+15)/3=3x+5

Subtract 5. 3x+5-5=3x

3x/x=3

The size of the resulting number is three times of

the size of the original number.