Word Problem

Question

Alice thought of a number, she multiplied the number by 3, then added 12. This result she divided by 3. Finally she subtracted 7. If her result was 6, what number was Alice thinking of?

Answer 1

What we don't know is the number Alice was thinking of.  That's usually a good place to start off with a variable.

 

A = Alice's number.

 

"she multiplied the number by 3"

 

3A

 

"then added 12"

 

3A + 12.

 

"This result she divided by 3." This is a little more tricky.  We need to use parenthesis to show that 3A + 12 happens BEFORE we divided by 3 (remember PEMDAS?)

 

(3A + 12)/3

 

"Finally, she subtracted 7."

 

(3A + 12)/3 - 7

 

"If her result was 6..."

 

(3A + 12)/3 - 7 = 6

 

"What number was Alice thinking of?"  ---->  Solve for A (Alice's number).

 

We can first add 7 to both sides:

 

(3A + 12)/3 = 13.

 

Next, we multiply both sides by 3 to clear the fraction on the left hand side:

 

(3A + 12) = 39.

 

We don't really need the parenthesis anymore:

 

3A + 12 = 39

 

Subtract 12 from both sides:

 

3A = 27

 

Divide both sides by 3:

 

A = 9.

 

Alice was thinking of the number 9.