SOLUTION: # 7. Pick any number and multiply the number by 2. Add 10 to the product. Divide the sum by 2. Subtract 5 from the quotient. Multiply the result by 7. What is the relationship

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: # 7. Pick any number and multiply the number by 2. Add 10 to the product. Divide the sum by 2. Subtract 5 from the quotient. Multiply the result by 7. What is the relationship      Log On


   

Question 190372: # 7. Pick any number and multiply the number by 2. Add 10 to the product. Divide the sum by 2. Subtract 5 from the quotient. Multiply the result by 7. What is the relationship between the number you started with and the final number. Select some different numbers and repeat the process. Make a conjecture about the original number and the final number.


Answer by jim_thompson5910(35256) About Me  (Show Source):
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# 7
Q: Pick any number and multiply the number by 2. Add 10 to the product. Divide the sum by 2. Subtract 5 from the quotient. Multiply the result by 7. What is the relationship between the number you started with and the final number. Select some different numbers and repeat the process. Make a conjecture about the original number and the final number.


A:


Let "x" be any number

Step 1) "Pick any number". I choose the number 2

Step 2) "...multiply the number by 2". 2*2 = 4

Step 3) "Add 10 to the product". 4 + 10 = 14

Step 4) "Divide the sum by 2". 14/2 = 7

Step 5) "Subtract 5 from the quotient". 7 - 5 = 2

Step 6) "Multiply the result by 7". 2 * 7 = 14

So after picking the number 2, the result after all of these operations is 14


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Step 1) "Pick any number". I choose the number 5

Step 2) "...multiply the number by 2". 5*2 = 10

Step 3) "Add 10 to the product". 10 + 10 = 20

Step 4) "Divide the sum by 2". 20/2 = 10

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

Step 6) "Multiply the result by 7". 5 * 7 = 35

So after picking the number 5, the result after all of these operations is 35


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Step 1) "Pick any number". I choose the number 11

Step 2) "...multiply the number by 2". 11*2 = 22

Step 3) "Add 10 to the product". 22 + 10 = 32

Step 4) "Divide the sum by 2". 32/2 = 16

Step 5) "Subtract 5 from the quotient". 16 - 5 = 11

Step 6) "Multiply the result by 7". 11 * 7 = 77

So after picking the number 11, the result after all of these operations is 77



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Step 1) "Pick any number". I choose the number 8

Step 2) "...multiply the number by 2". 8*2 = 16

Step 3) "Add 10 to the product". 16 + 10 = 26

Step 4) "Divide the sum by 2". 26/2 = 13

Step 5) "Subtract 5 from the quotient". 13 - 5 = 8

Step 6) "Multiply the result by 7". 8 * 7 = 56

So after picking the number 8, the result after all of these operations is 56


Are you starting to see a pattern?


Notice how at step 5, the result is the original number (for any number we choose). Then at step 6, we multiply that result by 7. So all we've done is take the original number and multiply it by 7.


So for ANY number "x" (the number we select), the result is 7x


Here's what's happening algebraically:

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

Step 2) "...multiply the number by 2". x%2A2+=+2x

Step 3) "Add 10 to the product". 2x%2B10

Step 4) "Divide the sum by 2". %282x%2B10%29%2F2=%282%28x%2B5%29%29%2F2=%28cross%282%29%28x%2B5%29%29%2Fcross%282%29=x%2B5

Step 5) "Subtract 5 from the quotient". %28x%2B5%29-5=x%2B5-5=x and we're back at the original number "x"

Step 6) "Multiply the result by 7". x%2A7=7x

So after picking the number "x", the result after all of these operations is 7x