"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.*