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.

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 $3$.

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.