Four fifth of a number is greater than three-fourths of the number by 4. Find the number.

Answer

To solve the problem step by step, let's break it down:

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

### Step 2: Set up the equation
According to the problem, four-fifths of the number is greater than three-fourths of the number by 4. This can be expressed mathematically as:
\[ \frac{4}{5}x - \frac{3}{4}x = 4 \]

### Step 3: Find a common denominator
To solve the equation, we need to find a common denominator for the fractions. The least common multiple (LCM) of 5 and 4 is 20. We will convert both fractions:
\[ \frac{4}{5}x = \frac{4 \times 4}{5 \times 4}x = \frac{16}{20}x \]
\[ \frac{3}{4}x = \frac{3 \times 5}{4 \times 5}x = \frac{15}{20}x \]

### Step 4: Substitute back into the equation
Now we can substitute these back into the equation:
\[ \frac{16}{20}x - \frac{15}{20}x = 4 \]

### Step 5: Simplify the equation
Combine the fractions on the left side:
\[ \frac{16x - 15x}{20} = 4 \]
This simplifies to:
\[ \frac{1}{20}x = 4 \]

### Step 6: Solve for \( x \)
To isolate \( x \), multiply both sides of the equation by 20:
\[ x = 4 \times 20 \]
\[ x = 80 \]

### Conclusion
The number is \( 80 \).

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