This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Mary's present age is 42 years, and Oloo's present age is 16 years. Steps: 1. Define variables: Let M be Mary's present age. Let O be Oloo's present age. 2. Formulate equations based on the given information: Condition 1: 3 years ago Mary was 3 times as old as Oloo. Mary's age 3 years ago: M - 3 Oloo's age 3 years ago: O - 3 Equation 1: M - 3 = 3(O - 3) M - 3 = 3O - 9 M = 3O - 6 Condition 2: In two years time the sum of their ages will be 62. Mary's age in 2 years: M + 2 Oloo's age in 2 years: O + 2 Equation 2: (M + 2) + (O + 2) = 62 M + O + 4 = 62 M + O = 58 3. Solve the system of equations: We have: 1) M = 3O - 6 2) M + O = 58 Substitute Equation 1 into Equation 2: (3O - 6) + O = 58 4O - 6 = 58 4O = 58 + 6 4O = 64 O = 64 / 4 O = 16 4. Find Mary's present age (M): Substitute O = 16 into Equation 2 (or Equation 1): M + 16 = 58 M = 58 - 16 M = 42 Therefore, Mary's present age is 42 years, and Oloo's present age is 16 years.