SOLUTION: # 2. Make a conjecture about the relationship between the original number and the final number in the following process. Pick a number. Multiply the number by 5 Add 10 to the

Question 190610: # 2. Make a conjecture about the relationship between the original number and the final number in the following process.
Pick a number.
Multiply the number by 5
Add 10 to the product
Divide the sum by 5
Subtract 1 from the quotient
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 2
Q: Make a conjecture about the relationship between the original number and the final number in the following process.
Pick a number.
Multiply the number by 5
Add 10 to the product
Divide the sum by 5
Subtract 1 from the quotient

A:
Let "x" be the unknown number

Example # 1

Step 1) "Pick any number". I choose the number 3

Step 2) "...multiply the number by 5". 3*5 = 15

Step 3) "Add 10 to the product". 15 + 10 = 25

Step 4) "Divide the sum by 5". 25/5 = 5

Step 5) "Subtract 1 from the quotient". 5 - 1 = 4

So after picking the number 3, the result after all of these operations is 4

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Example # 2

Step 1) "Pick any number". I choose the number 13

Step 2) "...multiply the number by 5". 13*5 = 65

Step 3) "Add 10 to the product". 65 + 10 = 75

Step 4) "Divide the sum by 5". 75/5 = 15

Step 5) "Subtract 1 from the quotient". 15 - 1 = 14

So after picking the number 13, the result after all of these operations is 14

------------------------------------------------

Example # 3

Step 1) "Pick any number". I choose the number 21

Step 2) "...multiply the number by 5". 21*5 = 105

Step 3) "Add 10 to the product". 105 + 10 = 115

Step 4) "Divide the sum by 5". 115/5 = 23

Step 5) "Subtract 1 from the quotient". 23 - 1 = 22

So after picking the number 23, the result after all of these operations is 22

Are you starting to see the pattern?

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Example # 4

Step 1) "Pick any number". I choose the number 9

Step 2) "...multiply the number by 5". 9*5 = 45

Step 3) "Add 10 to the product". 45 + 10 = 55

Step 4) "Divide the sum by 5". 55/5 = 11

Step 5) "Subtract 1 from the quotient". 11 - 1 = 10

So after picking the number 9, the result after all of these operations is 10

Notice how whatever number we choose, the result is simply the next number.

Conjecture: If our number is "x", then the result of these operations is

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Here's what's happening algebraically:

Step 1) "Pick any number". I choose the number "x"

Step 2) "...multiply the number by 5". x*5 = 5x

Step 3) "Add 10 to the product". 5x+10

Step 4) "Divide the sum by 5".

Step 5) "Subtract 1 from the quotient".

So after choosing the number "x", the result is
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