Three-fourths of a number exceeds two-thirds of the same number by 5. What is the number?

Introduction / Context:
This is another linear equation built from the difference of two fractional parts of a number. Solving requires careful fraction subtraction and then isolating the unknown. It checks comfort with least common multiples and proportional reasoning.

Given Data / Assumptions:

• (3/4)N − (2/3)N = 5.
• N is real and positive.
• We must find N.

Concept / Approach:
Subtract the fractions with a common denominator, then equate the result to 5 and solve for N. Using the identity (a/b − c/d) = (ad − bc) / bd helps to avoid errors.

Step-by-Step Solution:

Verification / Alternative check:
Check: (3/4)*60 = 45; (2/3)*60 = 40; 45 − 40 = 5. The condition holds perfectly.

Why Other Options Are Wrong:
48, 72, 84, and 36 yield differences other than 5 when substituted into the expression (3/4)N − (2/3)N.

Common Pitfalls:
Computing 3/4 − 2/3 incorrectly (e.g., 1/12 reversed in sign) or multiplying by the wrong reciprocal when isolating N.

Final Answer:
60