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

Answer:

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

Step-by-step 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: $\frac{88x + 88}{44} = \frac{88x}{44} + \frac{88}{44} = 2x+2$

Subtract 2: $2x + 2 - 2 = 2x$

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