Write a conjecture that relates the result of the process to the original number selected.

Question

The problem describes procedures that are to be applied to numbers. Repeat the procedure for four numbers of your choice. Write a conjecture that relates the result of the process to the original number selected.

 

Select a number. Multiply the number by 80. Add 80 to the product. Divide this sum by 40. Subtract 2 from the quotient.

 

a) The result is one more than double the original number.

b) The result is one more than the original number.

c) The result is double the original number.

d) The result is the original number.

 

The number I selected was 20 but I am not getting the right answer. I think its answer C? Can you also show the work so I can write it in my notes for future reference? Thanks!!

Answer 1

Hi, Pamela.  You are correct, the answer is C, and it should work for any four numbers you choose (assuming you're only using positive numbers).

 

A conjecture is just a fancy word for stating an unproven assumption.  In this case, you could say something like

"For any positive number, if you multiply this number by 80, add 80 to the product, divide this sum by 40 then subtract 2 from the quotient, the result will be double the original number."

 

Now for making sure you get the right answer, it helps to visualize the problem step by step.  Remember the key here is your order of operations:

 

1. Select a number (x):

x

2. Multiply the number (x) by 80:

x*80=80x

3. Add 80 to the product:

80x+80

4. Divide this sum by 40:

(80x+80)/40

5. Subtract 2 from the quotient:

(80x+80)/40-2

 

And that's the equation they've given you.  You can even simplify it if you want:

(80x+80) - 2 = 80x + 80 - 2 = 2x+2-2 = 2x

      40              40      40