SOLUTION: Follow the steps given, make a conjecture then prove your conjecture deductively: 1. Think of a number. **I chose 2 pls** 2. Multiply the number by 5 3. Add 17 to th

SOLUTION: Follow the steps given, make a conjecture then prove your conjecture deductively: 1. Think of a number. I chose 2 pls 2. Multiply the number by 5 3. Add 17 to th

Question 1184616: Follow the steps given, make a conjecture then prove your conjecture deductively:
1. Think of a number. **I chose 2 pls**
2. Multiply the number by 5
3. Add 17 to the result in Step 2.
4. Triple the result in Step 3.
5. Reduce the result in Step 4 by 6
6. Divide the result in Step 5 by 5
7. Subtract 9 from the result in Step 6.
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

See what happens with 2

1. Think of a number. **I chose 2 pls**
2. Multiply the number by 5.  **I get 10**
3. Add 17 to the result in Step 2.  **I get 27**
4. Triple the result in Step 3.     **I get 81**
5. Reduce the result in Step 4 by 6  **I get 75**
6. Divide the result in Step 5 by 5  **I get 15**
7. Subtract 9 from the result in Step 6  **I get 6**

I notice that 6 is 3 times the 2 that I started with.

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

See what happens with 10

1. Think of a number. **I chose 10 pls**
2. Multiply the number by 5.  **I get 50**
3. Add 17 to the result in Step 2.  **I get 67**
4. Triple the result in Step 3.     **I get 201**
5. Reduce the result in Step 4 by 6  **I get 195**
6. Divide the result in Step 5 by 5  **I get 39**
7. Subtract 9 from the result in Step 6  **I get 30**

I notice that 30 is 3 times the 10 that I started with.

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

See what happens with 7

1. Think of a number. **I chose 7 pls**
2. Multiply the number by 5.  **I get 35**
3. Add 17 to the result in Step 2.  **I get 52**
4. Triple the result in Step 3.     **I get 156**
5. Reduce the result in Step 4 by 6  **I get 150**
6. Divide the result in Step 5 by 5  **I get 30**
7. Subtract 9 from the result in Step 6  **I get 21**

Wow, 21 is 3 times 7, the number I started with.

So all three times I got 3 times what I started with.

So my conjecture is: You always get 3 times the number you choose.

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

So this time I'll choose a variable, which can stand for ANY number
and see what happens.

See what happens with variable N

1. Think of a number.

I choose 
N

2. Multiply the number by 5

I get 
5N

3. Add 17 to the result in Step 2.

I get 
5N + 17

4. Triple the result in Step 3.

I get 
3(5N + 17)
Simplify
15N + 51

5. Reduce the result in Step 4 by 6

I get
15N + 51 - 6
Simplify
15N + 45

6. Divide the result in Step 5 by 5

I get:

Simplify



7. Subtract 9 from the result in Step 6.

I get:
3N + 9 - 9
Simplify
3N

3N is 3 times N, the number I started with.

So now my conjecture is proved because N can be ANY number!

The proved conjecture is: You always get 3 times the number you choose.

Edwin

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