Identify the Number Using Fractions

The problem asks us to find a specific number. Let this unknown number be represented by the variable 'x'.

Set Up the Algebraic Equation

We are given that four-fifth of the number ('x') is 4 more than its three-fourth. We can write this relationship as an equation:

\(\frac{4}{5}x = \frac{3}{4}x + 4\)

Solve for the Number 'x'

To find the value of 'x', we need to isolate it. First, bring the terms involving 'x' to one side of the equation:

\(\frac{4}{5}x - \frac{3}{4}x = 4\)

Find a common denominator for the fractions, which is 20:

\((\frac{4 \times 4}{5 \times 4})x - (\frac{3 \times 5}{4 \times 5})x = 4\)

\(\frac{16}{20}x - \frac{15}{20}x = 4\)

Combine the fractions:

\(\frac{16 - 15}{20}x = 4\)

\(\frac{1}{20}x = 4\)

Now, solve for 'x' by multiplying both sides by 20:

\(x = 4 \times 20\)

\(x = 80\)

Verify the Solution

Let's check if the number 80 satisfies the condition:

• Four-fifth of 80: \(\frac{4}{5} \times 80 = 4 \times 16 = 64\)
• Three-fourth of 80: \(\frac{3}{4} \times 80 = 3 \times 20 = 60\)
• Difference: \(64 - 60 = 4\)

The difference is indeed 4, confirming our answer.