"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 "4x." Then, we add 3 to the answer, so 4x + 3. We then triplethe quantity "4x + 3": 3(4x + 3). Finally, we split the quantity 3(4x + 3) in half in order to yield the final answer, 12, so {3(4x+ 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 (4x + 3)} /2 = 12 (2) multiply both sides by 2...
{3(4x + 3)}/3 = 24/3divide 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