"Thinking backwards"-starting at the end of the problem and using reverse operations-can help you solve certain problems at different grade levels.

a) Write an equation that describes this problem.

b) What is the original number?

Answer:

a) We're looking for a certain (unidentified) number, *x. "x, quadrupled*" means "4*x.*" Then, we add 3 to the answer, so 4*x* + 3. We then *triple*the quantity "4*x *+ 3*"*: 3(4*x* + 3). Finally, we split the quantity 3(4*x* + 3) in *half *in order to yield the final answer, 12, so {3(4*x*+ 3)} /2 **= 12**.

b) To find the original number, we solve for *x*, which involves "canceling out" the numbers by using inverse operations.

So, (2){3 (4*x* + 3)} /2 = 12 (2) *multiply both sides by 2...*

{3(4x + 3)}/3 = 24/3*divide both sides by 3...*

4x + 3- 3 = 8 - 3* subtract 3 from both sides, and...*

4x /4= 5 /4 *divide both sides by 4.*

*Thus, x =* **1.25**