Question
The ages of two siblings, John and Mary, are in the
ratio of 5:3. Five years ago, the sum of their ages was 38 years. What are their current ages?Solution
Let John’s current age be 5x years and Mary’s current age be 3x years. According to the problem, five years ago: John's age = 5x - 5 Mary's age = 3x - 5 The sum of their ages five years ago was 38 years: (5x - 5) + (3x - 5) = 38 Simplifying the equation: 5x - 5 + 3x - 5 = 38 8x - 10 = 38 8x = 48 x = 6 Now, substituting x back to find their ages: John's age = 5x = 5(6) = 30 years Mary's age = 3x = 3(6) = 18 years
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