Nested fractions — Three-fourths of one-fifth of a number equals 60. Translate and solve for the number.

Introduction / Context:
Problems with nested fractions require careful reading. “Three-fourths of one-fifth of a number” means multiply the number by both fractions. Mastery of fraction multiplication and equation solving is the key here.

Given Data / Assumptions:

• Unknown number: n.
• (3/4)*(1/5)*n = 60.
• All operations are standard arithmetic over real numbers.

Concept / Approach:
Combine the fractions first, then invert the coefficient to isolate n. Keep fractions exact to avoid rounding errors and convert to integers only at the end if desired.

Step-by-Step Solution:
Compute combined fraction: (3/4)*(1/5) = 3/20.Equation: (3/20)*n = 60.Multiply both sides by 20/3: n = 60 * (20/3).Calculate: 60 * 20 = 1200; 1200 / 3 = 400 → n = 400.

Verification / Alternative check:
Check: one-fifth of 400 is 80; three-fourths of 80 is 60. The statement is satisfied exactly, confirming the solution.

Why Other Options Are Wrong:

• 300/450/1200/360: Substituting these into (3/20)*n does not yield 60; outcomes are different.

Common Pitfalls:
Misreading “of” as addition; multiplying by 4/3 instead of 20/3; arithmetic slips with 60 * 20. Work systematically to avoid mistakes.

Final Answer:
400