A teacher instructed her class to take any number and perform a series of computations using that number. The teacher was able to tell each student's original number by subtracting 1 from the student's answer. Create similar instructions for students so that the teacher needs to do only the following to obtain the student's original number:
A: Add 1 to the answer
B: Multiply the answer by 2
C: Multiply the answer by 1
Part A: Lets say the number any student chooses is 'x'. We need to perform operations to get to 'x-1'.
There are many possibilities for this. For example, consider the following scenario where the student is 's' and the teacher is 't'. I'll keep track of the number in the student category.
T: Select any number
S: 'x'
T: Divide that number by 2
S: x/2
T: Now add 4
S: (X/2) + 4
T: Now multiply by 2
S: "X + 8"
T: Now subtract 9
S: "x-1"
And now ask them to tell you what number they have and you know 'x' by adding one.
For parts B and C you do a similar process, you just want to arrive at "x/2" and "x" respectively.
I am lost on how to find these ways for it to equal out at the end with B and C. I don't understand these problems at all. :(
To create similar instructions for students, follow these steps:
1. Have the students choose any number as their starting point.
2. Instruct the students to perform the following computations using their chosen number:
Step A: Add 1 to the answer
Step B: Multiply the answer by 2
Step C: Multiply the answer by 1 (which is just multiplying it by itself, thus the number remains unchanged)
3. At the end of the computations, the teacher can obtain each student's original number by following these steps:
a. Subtract 1 from the student's final answer (which was obtained after performing Steps A, B, and C).
By subtracting 1 from the final answer, the teacher will be able to determine the student's original number.