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People use numbers every day to benefit themselves. Statistics can be misinterpreted simply because of the way the information is given. In the following questions, you will see how some of the number tricks work and learn to explain them by using algebra.

Here is an example of a trick:

- Choose a Number
- Add 5
- Double the result
- Subtract 4
- Divide the result by 2
- Subtract the number you started with
- The result is 3
Pick 4 different starting numbers and prove that the result will always be 3. Call these solutions Part A.

As we progress through our mathematical career we learn to use algebra more and do not accept a proof simply because it works for a bunch of random numbers.

Following is an algebraic proof of the above number trick. My original number is x:

Choose a number x Add five x + 5 Double the result 2(x + 5) or 2x + 10 Subtract 4 2x + 6 Divide by 2 x + 3 Subtract the original number 3

Find a similar algebraic proof for or each of the following number tricks. You can use any variable you want to start with, but you must always finish with a number. You must first find the resulting number.

## Question 1

Choose a number. Add 3. Multiply by 2. Add 4. Divide by 2. Subtract the number you started with. The result is ??## Question 2

Choose a number. Double it. Add 9. Add the number you started with. Divide by 3. Add 4. Subtract the number you started with. The result is ??## Question 3

Create a trick of your own. You must prove, using algebra, that your trick will always work.

Student solutions

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9 January 1996