Question

The following 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 88. Add 88 to the product. Divide this sum by 44. Subtract 2 from the quotient.

Answer 1

Conjecture: For every number x, the result of the is 2x

Explanation:

First Number: 8

Multiply by 88:
`88 * 8 = 704`

Add 88:
`704 + 88 = 792`

Divide by 44:
`792/44 = 18`

Subtract 2:
`18 - 2 = 16`

Second: 10

Multiply by 88:
`88 * 10 = 880`

Add 88:
`880+88=968`

Divide by 44:
`968/44=22`

Subtract 2:
`22-2=20`

Third: 5

Multiply by 88:
`88*5 = 440`

Add 88:
`440+88=528`

Divide by 44:
`528/44=12`

Subtract 2:
`12-2=10`

Fourth: 2

Multiply by 88:
`88*2=176`

Add 88:
`176+88=264`

Divide by 44:
`264/44=6`

Subtract 2:
`6-2=4`

On a general terms:

Let the number be x.

Multiply by 88:
`88x`

Add 88:
`88x + 88`

Divide by 44:
`(88x + 88)/(44) = (88x)/(44) + (88)/(44) = 2x+2`

Subtract 2:
`2x + 2 - 2 = 2x`

Notice that for every input x, the result is 2x