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
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-> 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
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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):
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.
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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.
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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.
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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