Question

a teacher asks the student to take any odd number, multiply by 4, add 16, and divide results by 2. subtract 7 from quotient and tell the answer. the teacher said she will be able to tell the student the original number. how?

Answer 1

Let x = an odd number and y=answer. Then the equation you just described would look like this:

y= ((x*4+16)/2)-7

If I told the teacher that my answer was 7, she could work backwards and find my original number:
x=(2(y+7)-16)/4
x=(2(7+7)-16)/4
x=(2(14)-16)/4
x=(28-16)/4
x=12/4
x=3

No matter what your answer will be she can use the second equation I wrote to find your original odd number.