Question

One-third of a number is 12 less than the
number itself

Answer 1

18

1/3n = n - 12
Subtract n from both sides
-2/3n = -12
Divide both sides by -2/3
n = 18

Answer 2

Explanation:

1. Set up an equation

This may be a word problem, but it can definitely be set up into an equation.

For this equation, we can use x as the number.

One-third of x, or x/3

IS (which can also mean equal, =)

12 less than the number itself, x-12

When you put these together you get:
x/3=x-12

We can then solve this equation like normal.

1. Multiply both sides by 3 to cancel the division

x=3x-36

2. subtract 3x on both sides

-2x=-36

3. Now divide each side by -2 to get rid of x's coefficient

x = 18

Test: We can check ourselves to see if this is correct.

1/3 of 18 is 6.

6 is also 12 less than 18.

This proves that 18 is the number.