Fraction comparison equation — A number is 25 more than its two-fifths. Form the equation and determine the number.

Introduction / Context:This problem uses a linear relationship between a number and a fraction of itself. Such problems test your ability to express relationships precisely and handle fractional coefficients in equations.

Given Data / Assumptions:

• Unknown number: n.
• Statement: n is 25 more than (2/5)*n.
• Equation: n = (2/5)*n + 25.

Concept / Approach:Move all n-terms to one side, constants to the other. Combine like terms and solve. Since the coefficient leads to a fractional result, the final answer may be a rational number rather than an integer.

Step-by-Step Solution:Start: n = (2/5)*n + 25.Subtract (2/5)*n from both sides: n - (2/5)*n = 25.Compute: (3/5)*n = 25.Solve: n = 25 * (5/3) = 125/3.

Verification / Alternative check:Compute two-fifths of 125/3: (2/5)*(125/3) = 250/15 = 50/3. Now 25 more than 50/3 is 50/3 + 25 = 50/3 + 75/3 = 125/3, which equals n, confirming correctness.

Why Other Options Are Wrong:

• 60/80/75/125/7: None satisfy n = (2/5)*n + 25 when substituted; the equality fails.

Common Pitfalls:Incorrectly adding 25 to the fraction without aligning denominators; moving terms to the wrong side; assuming the answer must be an integer. Rational results are perfectly valid.

Final Answer:125/3