
Method 1: Step 1: Convert the sentences into equations with different variables. Two equations with 2 variables or three equations with 3 variables etc Step 2: Solve the equations with variables to get the solution. Example: Emma is nine years older than Kate. Emma is four times as old as Betsy was three years ago. Betsy is eighteen years younger than Emma. How old is Kate? Solution: Let 'e' be the present age of Emma and 'k' and 'b' be the current ages of Kate and Betsy respectively. "Emma is nine years older than Kate" can be written as e = k + 9 "Emma is four times as old as Betsy was three years ago" can be written as: e  3 = 4(b3) "Betsy is eighteen years younger than Emma" can be written as: b = e  18 e = k + 9 e  3 = 4(b3) b = e  18 k = ? e  3 = 4(b3) substituting b = e  18 in the equation e  3 = 4(b3) e  3 = 4(e  183) e  3 = 4(e  21) e  3 = 4e  84 e  3 = 4e  84 3e = 81 e = 81/3 = 27 b = e  18 = 27  18 = 9 e = k + 9 => 27 = k+9 => k = 279 = 18 Emma is 27 years old, Betsy is 9 years and Kate is 18 years old. Verification: Emma is 9 years older than Kate: e = k + 9 = 18+9 = 27 Emma is four times as old as Betsy was three years ago. e  3 = 4(b3) 4(b3) = 4(93) = 4(6) = 24 e  3 = 27  3 = 24 Betsy is eighteen years younger than Emma: b = e  18= 27  18 = 9 Method 2: Step 1: Convert the sentences into equations with one variables. Step 2: Solve the equation with one variables to get the solution. Example: The age of the father is 4 years more than three times the age of son. Three years hence, father's age will be 16 years more than twice the age of his son. Determine their present ages. Solution: Let the present age of son = x years Father's age = 3x + 4 years Three years hence, son's age = x + 3 years Father's age = 3x + 4 + 3 = 3x + 7 years 3x + 7 = 2(x + 3) + 16 3x + 7 = 2x + 6 + 16 3x  2x = 6 + 16  7 x = 15 3x + 4 = 3 x 15 + 4 = 49 The son's age is 15 years and father's age = 49 years Directions: Solve the following word problems. You can use either of the methods to find the solution. 