How to Solve Age Problems Part 1

After a series of tutorials on word problems involving numbers, we now move to learning on how to solve word problems involving age. Age problems are very similar to number problems, so if you have finished reading The Number Word Problem Series, then it will be easier for you to solve the following age problems.

Example 1

Benjie is thrice as old as his son Cedric. The sum of their ages is 64. How old are both of them?

Scratch Work

This is one of those age problems that are very similar to number problems. Let’s take a specific case. If Cedric is say 8 years old, then Benji is 3(8) years old. This means that if Cedric is x years old, then Benjie is 3x. If we add their ages, the result is 64.

Solution

Let x be the age of Cedric and 3x be the age of Benjie.

Cedric’s Age + Benjie’s Age = 64

x + 3x = 64.

4x = 64

Dividing both sides of the equation by 4 gives us x = 16.

Therefore, Cedric is 16 and Benjie is 3(16) = 48 year sold.

Check

48 is thrice 16 and 48 + 16 = 64. So, we are correct.

Example 2

Karen is 6 years older than Nina. Five years from now, the sum of their ages will be 52. How old are both of them?

Scratch Work

If Nina is x years old, then Karen is 6 years older, so her age will be x + 6. Five years from now, both of their ages will increase by 5 as shown on the table below.

age problems

 Therefore, 5 years from now, the sum of their ages will be equal to

(x + 5) + x + 6 + 5 = 2x + 16. Now this sum is equal to 52.

Solution

Let x be Nina’s age and x + 5 be Karen’s age. In 5 years, Nina will be x + 5 years old and Karen will be x + 6 + 5 years old.

Now, (x + 5) + (x + 6 + 5) = 52

2x + 16 = 52

Subtracting 16 from both sides of the equation, we have

2x = 36

Dividing both sides by 2 we have

x = 18.

This means that Nina is 18 and Karen is 24.

Check

24 is 6 more than 18 and five years from now, (18 + 5) + (24 + 5) = 52. Therefore, we are correct.

Example 3

Sarah is twice as old as Jimmy. Three years ago, the sum of their ages is 39. How old are both of them now?

Scratch Work

If Jimmy is x years old, then Sarah’s age is twice his age, so Sarah is 2x years old. Three years ago, both are younger by 3 years, so both their ages must be subtracted by 3.

Screen Shot 2014-03-20 at 9.29.09 PM

 

Three years ago, the sum of their ages is 39. So, we add x -3 and 2x - 3 and equate it to 39

Solution

Let x be Jimmy’s age and 2x be Sarah’s age.

Three years ago, Jimmy was x - 3 years old and Sarah was 2x - 3 years old.

Three years ago, the sum of Jimmy’s and Sarah’s age is

(x - 3) + (2x - 3) = 39.

3x - 6 = 39

Adding 6 to both sides of the equation results to

3x = 45

Dividing both sides by 3, we have

x = 15.

So, Jimmy is 15 and Sarah is 30.

Check

Three years ago, Jimmy was 15 - 3 = 12 years old and Sarah was 30 - 3 = 27 years old. The sum of their ages was 12 + 27 = 39.

That’s all for now, we discuss more problems in the next post.

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3 Responses

  1. August 7, 2014

    […] ← How to Solve Age Problems Part 1 How to Solve Age Problems Part 3 → […]

  2. August 20, 2015

    […] How to Solve Age Problems Part 1 discusses simple 2-person problems particularly present-past and present-future age relationships. […]

  3. August 20, 2015

    […] that are not discussed in the first two parts. We have already solved six problems in the first and second part, so we start with the seventh […]

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