MathWhiz likes to play a fun number trick on her friends. She tells them to think of a number. She then tells them to subtract their number from 1 and multiply the result by 4. To this product she tells them to add half the difference when 6 is subtracted from 10 times their original number.
(a) If I use the number 3 and follow MathWhiz's steps, what number will I get?
(b) If you correctly apply MathWhiz's steps to any number, and then tell MathWhiz your result, how can MathWhiz quickly figure out what number you started with?
+23254 Let X be the original number.
Subtract that number from 1 ---> 1 - X
Multiply this result by 4: ---> 4(1 - X)
Add half the difference when 6 is subtracted from 10 times the original number:
---> 4(1 - X) + ½(10X - 6)
Final result: ---> 4 - 4X + 5X - 3 = X + 1
a) Let X = 3: ---> X + 1 = 4
b) To find the original number from the answer: Subtract 1.
