Pick anynumber, multiply the number by 3, add 18 to theproduct, divide the sum by 3, and subtract 6 from the quotient Complete parts a through d below a) What is the relationship between the number you started with and the finalnumber A The final number is 13 of the original number B The final number is the same as the original number C The final number is 12 more than the original number D The final number is 3 times the original number b) Arbitrarily select some different number and repeat theprocess, recording the original number and the result A The final number is 3 times the original number B The final number is the same as the original number C The final number is 13 of the original number D The final number is 12 more than the original number c) Can you make a conjecture about the relationship between the original number and the finalnumber A The final number is always 12 more than the original number B The final number is always 3 times the original number C The final number is always 13 of the original number D The final number is always the same as the original number d) Try toprove, using deductivereasoning, the conjecture you made in part(c) A Pick a number n Multiply the number by 3, 3n Add 18 to theproduct, 3n 18 Divide the sum by 3, 3n 183 n 6 Subtract 6 from thequotient, n 66 n B Pick a number n Multiply the number by 3, 3n Add 18 to theproduct, 3n 18 Divide the sum by 3, 3n 183 3n 6 Subtract 6 from thequotient, 3n 66 3n C Pick a number n Multiply the number by 3, 3n Add 18 to theproduct, 3n 18 Divide the sum by 3, 3n 183 n3 6 Subtract 6 from thequotient, n3 66 n3 D Pick a number n Multiply the number by 3, 3n Add 18 to theproduct, 3n 18 Divide the sum by 3, 3n3 18 n 18 Subtract 6 from thequotient, n 186 n 12

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Pick anynumber, multiply the number by 3, add 18 to theproduct, divide the sum by 3, and subtract 6 from the quotient. Complete parts a

Pick anynumber, multiply the number by 3, add 18 to theproduct, divide the sum by 3, and subtract 6 from the quotient. Complete parts a through d below

a) What is the relationship between the number you started with and the finalnumber?

The final number is 13 of the original number.

The final number is the same as the original number.

The final number is 12 more than the original number.

The final number is 3 times the original number.

b) Arbitrarily select some different number and repeat theprocess, recording the original number and the result.

The final number is 3 times the original number.

The final number is the same as the original number.

The final number is 13 of the original number.

The final number is 12 more than the original number.

c) Can you make a conjecture about the relationship between the original number and the finalnumber?

The final number is always 12 more than the original number.

The final number is always 3 times the original number.

The final number is always 13 of the original number.

The final number is always the same as the original number.

d) Try toprove, using deductivereasoning, the conjecture you made in part(c).

Pick a number n. Multiply the number by 3, 3n. Add 18 to theproduct, 3n+18. Divide the sum by 3, 3n+183=n+6. Subtract 6 from thequotient, n+66=n.

Pick a number n. Multiply the number by 3, 3n. Add 18 to theproduct, 3n+18. Divide the sum by 3, 3n+183=3n+6. Subtract 6 from thequotient, 3n+66=3n.

Pick a number n. Multiply the number by 3, 3n. Add 18 to theproduct, 3n+18. Divide the sum by 3, 3n+183=n3+6. Subtract 6 from thequotient, n3+66=n3.

Pick a number n. Multiply the number by 3, 3n. Add 18 to theproduct, 3n+18. Divide the sum by 3, 3n3+18=n+18. Subtract 6 from thequotient, n+186=n+12.