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
Here's how to solve the problem: The given proportion is: (3)/(7) = (27)/(A) = (B)/(105) Step 1: Find the value of A. We use the first two parts of the proportion: (3)/(7) = (27)/(A) To solve for A, we can cross-multiply: 3 × A = 27 × 7 3A = 189 Divide both sides by 3: A = (189)/(3) A = 63 Step 2: Find the value of B. We use the first and third parts of the proportion: (3)/(7) = (B)/(105) To solve for B, we can cross-multiply: 3 × 105 = 7 × B 315 = 7B Divide both sides by 7: B = (315)/(7) B = 45 So, the values are A = 63 and B = 45. Comparing this with the given options: (A) A = 9, B = 45 (B) A = 9, B = 15 (C) A = 63, B = 45 (D) A = 63, B = 15 The correct option is (C). The final answer is C