The present ages of three persons are in proportions 4 : 7 : 9.Eight years ago, the sum of their ages was 76.Find their present ages (in years).
Question
The present ages of three persons are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 76. Find their present ages (in years).
Solution
Let's denote the present ages of the three persons as 4x, 7x, and 9x.
Step 1: Calculate their ages 8 years ago. Their ages 8 years ago would be 4x - 8, 7x - 8, and 9x - 8.
Step 2: Set up the equation. According to the problem, the sum of their ages 8 years ago was 76. So, we can set up the following equation: (4x - 8) + (7x - 8) + (9x - 8) = 76
Step 3: Simplify the equation. This simplifies to 20x - 24 = 76
Step 4: Solve for x. Add 24 to both sides of the equation to get 20x = 100. Then, divide both sides by 20 to solve for x. x = 5.
Step 5: Find their present ages. Substitute x = 5 into 4x, 7x, and 9x to get their present ages. The present ages of the three persons are 20 years, 35 years, and 45 years respectively.
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