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Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
3.14 Word Problems - Age - 6

Example:
Twenty-five years ago, Hailey was five more than one-third as old as Jason was. Today, Jason is twenty-six less than two times the age of Hailey. How old is Jason?
Solution:
Let 'j' and 'h' are present ages of Jason and Hailey.
Twenty-five ago their ages are j-25 and h-25
Twenty-five years ago, Hailey was five more than one-third as old as Jason was can be written as: h - 25 = 1/3 (j-25) + 5
Today, Jason is twenty-six less than two times the age of Hailey: j = 2h - 26
h - 25 = 1/3 (j-25) + 5
j = 2h - 26
h - 25 = 1/3 (j-25) + 5
h - 30 = 1/3 (j-25)
3h - 90 = j - 25
3h = j - 25 + 90
3h = j + 65
substituting j = 2h - 26 in the above equation we have
3h = 2h - 26 + 65
3h - 2h = - 26 + 65
h = 39
j = 2h - 26 = 2 x 39 - 26 = 52
Jason is 52 years and Hailey is 39 years old.

Example:
Harry is five times as old as Ron. Tom is twice as old as Ron. Ron is twelve years younger than Tom. How old is Harry?
Solution:
Let 'h' 'r' and 't' be the present ages of Harry, Ron and Tom respectively.
Given:
h = 5r
t = 2r
r = t-12
Solve:
r = t-12
r = 2r - 12
12 = 2r - r
12 = r
h = 5r = 5x12 = 60
Harry is 60 years old.

Directions: Solve the following word problems.
Q 1: In 4 years, Cathy's age will be the same as Ted's age now. In 2 years, Ted will be twice as old as Cathy. Find their ages now.
Ted is 8 and Cathy is 4
Ted is 6 and Cathy is 2
Ted is 10 and Cathy is 6

Q 2: Sally is twice as old as Cody. If 16 is added to Cody's age and 16 is subtracted form Sally's age, their ages will then be equal. What are their present ages?
Cody is 30 and Sally is 60
Cody is 32 and Sally is 64
Cody is 28 and Sally is 64

Question 3: This question is available to subscribers only!

Question 4: This question is available to subscribers only!


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