algebra math trick

Question

pick an integer from 1-10, double the #, add 5, pick another #, add those two together, subtract 25 and you are left with a double digit number the first digit being the first integer they picked and the second digit being the second integer picked. how does this work.

Answer 1

1. In this type of simple math trick, really you want to do is shift the first number so that it shows up in the ten's place.  This can be done by multiplying it by 10.  But this would be so straightforward, then you need to do a few steps, which ultimately does the same thing (i.e., multiply by 10).  But the effect of these additional steps is to try and confuse the person who is participating in the trick.  I'm not sure what you intended, but here is a slight variation.  I think you may have left out step 6.
2. In the following steps, the correct order of the steps is shown, along with the algebraic expression, and the value of the number when the first number selected is 3 and the second number selected is 8.
3. Pick an integer between 0 and 10. {In other words, you can pick 1, 2...9} Let this number =x
4. Double the number.  2x.   [2*3 = 6]
5. Add 5.  2x+5 [6+5 =11]
6. Multiply by 5.  5(2x+5) = 10x + 25.   [55]
7. Add the second number y.   10x+25+y =  [63]
8. Subtract 25.  10x + 25 + y - 25.  [63-25 = 38]
9. first digit = 3, and second digit = 8

 

So, you can see the trick was to shift the first number in the ten's place (by multiplying it first by 2 and then by 5) and then adding 25 to that (by multiplying 5*5 in steps 5 & 6.  Then the last step (step 8) subtracts out the 25 that was added.