A + a + a = 30 b + b + a = 20 c + c + b = 13 a + b × c = ?

To solve for \( a + b \times c \) given the equations: 1. \( a + a + a = 30 \) 2. \( b + b + a = 20 \) 3. \( c + c + b = 13 \) Let's solve each equation step by step. From equation 1: \[ 3a = 30 \implies a = \frac{30}{3} = 10 \] Now, substituting \( a = 10 \) into equation 2: \[ b + b + 10 = 20 \] \[ 2b + 10 = 20 \implies 2b = 20 - 10 \implies 2b = 10 \implies b = \frac{10}{2} = 5 \] Next, substitute \( b = 5 \) into equation 3: \[ c + c + 5 = 13 \] \[ 2c + 5 = 13 \implies 2c = 13 - 5 \implies 2c = 8 \implies c = \frac{8}{2} = 4 \] Now we have the values: - \( a = 10 \) - \( b = 5 \) - \( c = 4 \) Now we can calculate \( a + b \times c \): \[ b \times c = 5 \times 4 = 20 \] \[ a + b \times c = 10 + 20 = 30 \] Thus, the answer is: \[ \boxed{30} \]