A is twice as old as B. B is 1/3 as old as C. The sum of ages of A, B, and C is 42 years. Find the sum of the ages of A and B.

Explanation

Let's solve this problem step-by-step. Step 1: Define the Variables Let: BBB's age be xxx. Since AAA is twice as old as BBB, AAA's age is 2x2x2x. BBB is 1/3 as old as CCC, so CCC's age is 3x3x3x. Step 2: Set Up the Equation The sum of the ages of AAA, BBB, and CCC is 42 years. 2x+x+3x=422x + x + 3x = 422x+x+3x=42 Step 3: Simplify the Equation Combine like terms: 6x=426x = 426x=42 Step 4: Solve for xxx x=426=7x = \frac{42}{6} = 7x=642​=7 Step 5: Find the Ages of AAA and BBB BBB's age =x=7= x = 7=x=7 AAA's age =2x=2×7=14= 2x = 2 \times 7 = 14=2x=2×7=14 Step 6: Calculate the Sum of the Ages of AAA and BBB A+B=14+7=21A + B = 14 + 7 = 21A+B=14+7=21 Answer: The sum of the ages of AAA and BBB is 21 years.