The present ages of A, B and C are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. What are their present ages (in years)?
Question
The present ages of A, B and C are in proportions 4 : 7 : 9.
Eight years ago, the sum of their ages was 56. What are their present ages (in years)?
Solution
Step 1: Let's assume the present ages of A, B, and C are 4x, 7x, and 9x respectively.
Step 2: According to the problem, eight years ago, the sum of their ages was 56. So, we can write the equation as (4x-8) + (7x-8) + (9x-8) = 56.
Step 3: Simplify the equation: 20x - 24 = 56.
Step 4: Add 24 to both sides of the equation: 20x = 80.
Step 5: Divide both sides of the equation by 20 to solve for x: x = 4.
Step 6: Substitute x = 4 into the expressions for the ages of A, B, and C to find their present ages: A = 44 = 16 years, B = 74 = 28 years, C = 9*4 = 36 years.
So, the present ages of A, B, and C are 16 years, 28 years, and 36 years respectively.
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