Find a number such that one - fifth of it is less than its one - fourth by 3.

Answer

To solve the problem, we need to find a number such that one-fifth of it is less than one-fourth of it by 3. Let's break this down step by step.

### Step 1: Define the variable
Let the unknown number be \( x \).

### Step 2: Write the expressions
According to the problem:
- One-fifth of the number is \( \frac{x}{5} \).
- One-fourth of the number is \( \frac{x}{4} \).

### Step 3: Set up the inequality
The problem states that one-fifth of the number is less than one-fourth of the number by 3. This can be expressed as:
\[ \frac{x}{5} + 3 = \frac{x}{4} \]

### Step 4: Solve the equation
To eliminate the fractions, we can find a common denominator. The least common multiple of 5 and 4 is 20. We will multiply each term by 20:
\[ 20 \left(\frac{x}{5}\right) + 20 \cdot 3 = 20 \left(\frac{x}{4}\right) \]
This simplifies to:
\[ 4x + 60 = 5x \]

### Step 5: Rearrange the equation
Now, we will rearrange the equation to isolate \( x \):
\[ 60 = 5x - 4x \]
\[ 60 = x \]

### Step 6: Conclusion
Thus, the number we are looking for is:
\[ \boxed{60} \]

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