This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Define variables for the number of ducks and goats. Let D be the number of ducks. Let G be the number of goats. Step 2: Formulate equations based on the given information. Each animal has 1 head. So, the total number of heads is: D + G = 77 (Equation 1) Ducks have 2 legs each, and goats have 4 legs each. So, the total number of legs is: 2D + 4G = 224 (Equation 2) Step 3: Solve the system of equations for D. From Equation 1, express G in terms of D: G = 77 - D Substitute this expression for G into Equation 2: 2D + 4(77 - D) = 224 2D + 308 - 4D = 224 -2D = 224 - 308 -2D = -84 D = (-84)/(-2) D = 42 The number of ducks is 42. The correct option is (A). The number of ducks is 42. Send me the next one 📸