Question

Jill is trying to prove the following number trick: Choose any number. Add 3. Double it. Add 4. Divide by 2. Take away the number you started with. Each time Jill tries the trick, she ends up with 5. Clearly demonstrate a proof by:

a) inductive reasoning:

b) deductive reasoning:

Answer 1

a)Inductive reasoning proof

Think of a number: 4

add 3: $4+3=7$

Double it: $14$

Add 4: $18$

Divide by 2: $\frac{18}{2}=9$

Take away the number you started with: $9-4=5$

b) deductive reasoning proof

Think of a number: $n$

add 3: $n+3$

Double it: $(n+3)2=2n+6$

Add 4: $2n+6+4=2n+10$

Divide by 2: $\frac{2n+10}{2}=n+5$

Take away the number you started with: $n+5-n=5$