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### Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation3.10 Word Problems - Age - 2

 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(b-3) "Betsy is eighteen years younger than Emma" can be written as: b = e - 18 e = k + 9 e - 3 = 4(b-3) b = e - 18 k = ? e - 3 = 4(b-3) substituting b = e - 18 in the equation e - 3 = 4(b-3) e - 3 = 4(e - 18-3) 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 = 27-9 = 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(b-3) 4(b-3) = 4(9-3) = 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. Identify the unknown. It is the variable you want to find out. Write the first equation and all other equations with respect to the same variable. 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.
 Q 1: Amy's father is 4 times as old as Amy. In 10 years, Amy's father will be 3 times as old as Amy. What are their ages? Amy is 14 years and her father is 77 yearsAmy is 20 years and her father is 80 yearsAmy is 15 years and her father is 60 years Q 2: Harry is 25 years older than Peter. In 5 years, Harry will be 2 times as old as Peter will be then. What are their present ages? Harry is 41 and Peter is 12 yearsHarry is 52 and Peter is 22 yearsHarry is 45 and Peter is 20 years Q 3: The sum of Greg's age and Joe's age is 66 years. In 5 years from now, Greg's age will be 2 times Joe's age 2 years ago. Find their present ages. Greg is 40 years and Joe is 26 yearsGreg is 41 years and Joe is 25 yearsGreg is 25 years and Joe is 41 years Q 4: Jill is twice as old as Lisa. 5 years ago, Jill was thrice as old as Lisa was then. Find their present ages. Lisa is 15 years and Jill is 30 yearsLisa is 10 years and Jill is 20 yearsLisa is 11 years and Jill is 22 years Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!