Question 134143
One-third of a number is 5 less than half of the same number. What is the number?

Let x = the missing number

1/3(x) = (1/2)(x) - 5

We now solve for x.

(1/3)(x) can be written as simply x/3.

(1/2)(x) can be written as simply x/2.

We now have a fractional equation:

x/3 = x/2 - 5....Much easier to work with, right?

To remove the fractions, we multiply both sides of the equation by the LCD, which is 6.

x/3 times 6 = 2x

x/2 times 6 = 3x

-5 times 6 = -30

We now have a linear equation:

2x = 3x - 30

Subtract 3x from 2x.

2x - 3x = -30

-x = -30

Divide both sides by -1 to find our missing number.

x = -30/-1

x = 30

So, what is the missing number?  The missing number is 30.