Number system — If three-fourths (3/4) of a number is 19 less than the original number, find the value of that number. Show clear reasoning using a simple linear equation.

Introduction / Context:
This is a classic one-variable linear equation problem from number systems. The phrase “three-fourths of a number is 19 less than the original number” translates directly into an equation that can be solved with basic algebra. These questions test your ability to convert verbal statements into symbolic form and manipulate fractions confidently.

Given Data / Assumptions:

• Let the unknown number be n.
• Three-fourths of the number means (3/4) * n.
• “Is 19 less than the original number” means equals n - 19.
• We assume n is a real number (solution will be an integer here).

Concept / Approach:
Translate words to an equation and isolate n. Fractional coefficients are handled by moving terms to one side and using basic operations. Keep track of units and signs carefully to avoid simple mistakes.

Step-by-Step Solution:
Form the equation: (3/4)*n = n - 19.Move terms: n - (3/4)*n = 19.Compute left side: (1/4)*n = 19.Solve for n: n = 19 * 4 = 76.

Verification / Alternative check:
Check n = 76. Three-fourths of 76 is 57. Then n - 19 = 76 - 19 = 57. Both sides match (57), so the solution is consistent.

Why Other Options Are Wrong:

• 84/64/72/68: These values do not satisfy (3/4)*n = n - 19 when substituted; the two sides will differ.

Common Pitfalls:
Forgetting that “19 less than n” is n - 19 (not 19 - n); mishandling fractions when moving terms; multiplying by 4 incorrectly. Keep the algebraic steps neat to avoid sign errors.

Final Answer:
76