Here's how to solve the problem: The given proportion is: $$ \frac{3}{7} = \frac{27}{A} = \frac{B}{105} $$ Step 1: Find the value of A. We use the first two parts of the proportion: $$ \frac{3}{7} = \frac{27}{A} $$ To solve for A, we can cross-multiply: $$ 3 \times A = 27 \times 7 $$ $$ 3A = 189 $$ Divide both sides by 3: $$ A = \frac{189}{3} $$ $$ A = 63 $$ Step 2: Find the value of B. We use the first and third parts of the proportion: $$ \frac{3}{7} = \frac{B}{105} $$ To solve for B, we can cross-multiply: $$ 3 \times 105 = 7 \times B $$ $$ 315 = 7B $$ Divide both sides by 7: $$ B = \frac{315}{7} $$ $$ B = 45 $$ 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 $\boxed{\text{C}}$