Pick any number and add 4 to it. Find the sum of the new number and the original number. Add 6 to the sum. Divide the new sum by 2 and subtract the original number from the quotient. Complete parts​ a) through​ d) below.

​a) What is the final​ number?
The final number is
  
5.
Part 2
​b) Arbitrarily select some different numbers and repeat the​ process, recording the original number and the results.
The final number is
  
5.
Part 3
​c) Can you make a conjecture about the relationship between the original number and the final​ number?
A.
The final number is always 4 times the original number.
B.
The final number is always the same as the original number.
C.
The final number is always 5.
D.
The final number is always one fourth
of the original number.
Part 4
​d) Try to​ prove, using deductive​ reasoning, the conjecture you made in part​ (c).
A.
Pick a number n. Add 4 to the​ number, nplus4. Add this value to the original​ number, 2 n plus 4. Add 6 to this​ value, 2 n plus 10. ​Next, divide this value by​ 2, nplus5. Then subtract the original​ number, n, from this to reach the final​ number, 5.
B.
Pick a number n. Add 4 to the​ number, nplus4. Add this value to the original​ number, 2 n plus 4. Add 6 to this​ value, 2 n plus 10. ​Next, divide this value by​ 2, nplus5. Then subtract 5 from this and divide by 4 to reach the final​ number, one fourth
n.
C.
Pick a number n. Add 4 to the​ number, nplus4. Add this value to the original​ number, 2 n plus 4. Add 6 to this​ value, 2 n plus 10. ​Next, divide this value by​ 2, nplus5. Then subtract 5 from this and multiply by 4 to reach the final​ number, 4n.
D.
Pick a number n. Add 4 to the​ number, nplus4. Add this value to the original​ number, 2 n plus 4. Add 6 to this​ value, 2 n plus 10. ​Next, divide this value by​ 2, nplus5. Then subtract 5 from this to reach the final​ number, n.