Lesson Age problems and their solutions

Age problems

The purpose of this lesson is to show you how to solve Age problems.

Problem 1

Kevin is 4 years older than Margaret.
Next year Kevin will be 2 times as old as Margaret.
How old is Kevin?

Solution
Denote as Kevin's present age.
Then Margret's present age is .

Next year Kevin will be years old, and Margaret will be years old.

Since next year Kevin will be 2 times as old as Margaret, you can write the equation
.

Solve this equation by simplifying it, step by step:

  (after brackets opening at the right side)
  (after moving variable terms to the right and constant terms to the left)
            (after combining like terms)

Thus, you got that Kevin's present age is years.

Check.
If Kevin's present age is 7 years, then Margaret is years old now.
Next year Margaret will be 4 years old, while Kevin will be 8 years old, which means that next year Kevin will be 2 times as old as Margaret.
The solution is correct.

Answer. Kevin is 7 years old now.

Problem 2

Ann is 2 years older than Betty.
Last year Ann was 2 times as old as Betty.
How old is Ann?

Solution
Denote as Ann's present age.
Then Betty's present age is .

Last year Ann was years old, and Betty was years old.

Since last year Ann was 2 times as old as Betty, you can write the equation
.

Solve this equation by simplifying it, step by step:

  (after brackets opening at the right side)
  (after moving variable terms to the right and constant terms to the left)
            (after combining like terms)

Thus, you got that Ann's present age is years.

Check.
If Ann's present age is 5 years, then Betty is years old now.
Last year Ann was 4 years old, while Betty was 2 years old, which means that last year Ann was 2 times as old as Betty.
The solution is correct.

Answer. Ann is 5 years old now.

Problem 3

Susan is 3 years older than Tom. Two years ago Susan was twice as old as Tom.
Find their present ages.

Solution
Denote as Tom's age 2 years ago.
Then Susan's age was 2 years ago.

Tom's age is at present.
Susan's age is at present.

Since Susan is 3 years older than Tom, you can write the equation
.

Solve this equation by simplifying it, step by step:
  (after combining like terms at the right side)
  (after moving variable terms to the right and constant terms to the left)
            (after combining like terms)

Thus, you got that Tom was years old two years ago.
Hence, Susan was years old at that time.
At present, Tom is years old, and Susan is years old.

Answer. At present, Tom is 5 years old, and Susan is 8 years old.

Problem 4

Jerry is 7 years older than Jennifer. In three years Jerry will be twice as old as Jennifer.
Find their present ages.

Solution
Denote as Jennifer's present age.
Then Jerry's present age is .

In three years Jennifer's age will be , while Jerry's age in three years will be .
Since in two years Jerry will be twice as old as Jennifer, you can write the equation
.

Solve this equation by simplifying it, step by step:
  (after brackets opening at the right side)
  (after moving variable terms to the right and constant terms to the left)
             (after combining like terms)

Thus, you got that Jerry's present age is years.
Hence, Jennifer's present age is years.

In three years, Jerry will be years old, while Jennifer will be years old.

Answer. At present, Jerry is 4 years old, and Jennifer is 11 years old.

Problem 5

A man has a daughter and a son.
The son is three years older than the daughter.
In one year the man will be six time as old as the daughter is now.
In ten years the man will be fourteen years older than the combined ages of his children at that time.
What is the man's present age?

Solution
Denote as the daughter's present age.
Then the son's present age is .

Since in one year the man will be six time as old as the daughter is now, the man's present age is .
In ten years the man's age will be , while the daughter's age will be and the son's age will be .

Since in ten years the man will be fourteen years older than the combined ages of his children at that time, you can write an equation
.

Solve this equation by simplifying it, step by step:
  (after combining like terms at the right side)
  (after moving variable terms to the right and constant terms to the left)
            (after combining like terms)
.

Thus, you got that the daughter's present age is years.
Hence, the son's present age is years, and the man's present age is .

Answer. At present, the man is 41 years old.