We need to find a number such that when $\frac{1}{4}$ of it is subtracted from $\frac{1}{3}$ of it, the result is 12.

1. Problem Description

We need to find a number such that when $\frac{1}{4}$ of it is subtracted from $\frac{1}{3}$ of it, the result is

1

2.

2. Solution Steps

Let the number be $x$. We are given that:

$\frac{1}{3}x - \frac{1}{4}x = 12$

To solve for $x$, we first find a common denominator for the fractions $\frac{1}{3}$ and $\frac{1}{4}$. The least common denominator (LCD) of 3 and 4 is

1

2. We rewrite the fractions with the common denominator:

$\frac{4}{12}x - \frac{3}{12}x = 12$

Now we can combine the terms with $x$:

$(\frac{4}{12} - \frac{3}{12})x = 12$

$\frac{1}{12}x = 12$

To isolate $x$, we multiply both sides of the equation by 12:

$12 \times \frac{1}{12}x = 12 \times 12$

$x = 144$

3. Final Answer

The number is 144.