The mother is twice as old as her daughter. The daughter is 6 years younger than her uncle. The sum of their ages was 87 years five years ago. What are their present ages?

Here's how to solve the age problem: Step 1: Define variables for their present ages. Let M be the mother's present age. Let D be the daughter's present age. Let U be the uncle's present age. Step 2: Formulate equations based on the given information. From the first statement, "The mother is twice as old as her daughter": M = 2D (Equation 1) From the second statement, "The daughter is 6 years younger than her uncle": D = U - 6 This can be rewritten as: U = D + 6 (Equation 2) From the third statement, "The sum of their ages was 87 years five years ago": Five years ago, their ages were M-5, D-5, and U-5. (M-5) + (D-5) + (U-5) = 87 M + D + U - 15 = 87 M + D + U = 87 + 15 M + D + U = 102 (Equation 3) Step 3: Solve the system of equations. Substitute Equation 1 (M=2D) and Equation 2 (U=D+6) into Equation 3: (2D) + D + (D+6) = 102 Combine like terms: 4D + 6 = 102 Subtract 6 from both sides: 4D = 102 - 6 4D = 96 Divide by 4 to find the daughter's present age: D = (96)/(4) D = 24 The daughter's present age is 24 years. Step 4: Calculate the mother's and uncle's present ages. Using Equation 1 to find the mother's age: M = 2D = 2 × 24 M = 48 The mother's present age is 48 years. Using Equation 2 to find the uncle's age: U = D + 6 = 24 + 6 U = 30 The uncle's present age is 30 years. The present ages are: Mother: 48 years old Daughter: 24 years old Uncle: 30 years old