“A number multiplied by three-fourths of itself equals 10800. What is the number?”

"Let the number be x. The equation is x * (3/4)x = 10800 or (3/4)x² = 10800. Multiplying both sides by 4/3 x² = 14400 so x = ±120. Since the context implies a positive number x = 120. This quadratic equation showcases algebraic problem-solving commonly applied in areas like economics and engineering where relationships between variables must be quantified accurately to derive precise solutions."