Instructions: DO NOT USE CALCULATOR. Figures are not drawn to scale. One-fourth of a number is equal to two-fifth of another number. If 50 is added to the larger number, it becomes two times the second number. What is the smaller number?
Explanation: (D) Let X be the larger number and Y be the smaller number. Equation 1: \(\frac{1}{4}X = \frac{2}{5}Y \implies 5X = 8Y\). Equation 2: \(X + 50 = 2Y\). Substituting \(X = \frac{8}{5}Y\) into Equation 2: \(\frac{8}{5}Y + 50 = 2Y \implies 50 = 2Y - \frac{8}{5}Y = \frac{10Y - 8Y}{5} = \frac{2Y}{5}\). So, \(2Y = 250 \implies Y = 125\). The smaller number is 125.
