# Math Word Problems: Solving Age Problems Part 2

This is the second part of the 3-part installment posts on Solving Age Problems in the Math Word Problem Solving Series.

In this post, we continue with three more worked examples on age problems.  The first part of this series can be read here.

PROBLEM 4

Janice is four times as old as his son. In $5$ years, she will be as three times as old as his son. What is Janice’s present age?

Solution

Let $x$ be the present age of Janice’s son and 4x be her age. According to the problem, in five years, she will be three times as old as her son. In five years, Janice age will be $4x + 5$ and her son’s age will be $x+5$. If she is three times as old as her son, if we multiply her son’s age by $3$, their ages will be equal. That is, $3(x + 5) = 4x + 5$.

Simplifying, we have $3x + 15 = 4x + 5$ giving us $x = 10$. Therefore, the son is $10$ years old and Janice is $40$ years old.

The present ages of Janice and her son are $40$ and $10$ respectively. Yes, she is four times as old as here son.  In $5$ years, Janice will be $45$ and her son will be $15$.  Since $45$ is three times $15$, we are correct.

Problem 5

Vince is thrice as old as Albert. Vince age $5$ years from now will be equal to Albert’s age $13$ years from now. What are their present ages?

Solution

Let $x$ be present age of Albert and $3x$ be the present age of Vince. Vince’s age five years from now will be $3x + 5$. This will be equal to  Albert’s age $13$ years from now which is $x + 13$. So, we set up the equation $3x + 5 = x + 13$.

This gives us $2x = 8$ and $x = 4$.

Left as an exercise.

PROBLEM 6

Anna is thrice as old as Karen and Nina is $5$ years older than Karen. In $3$ years, the sum of Karen and Nina’s age will be $5$ more than Anna’s age. What are their ages?

Solution

Let $x$ be Karen’s age, $3x$ be Anna’s age and $x + 5$ be Nina’s age. In three years, their ages will be

Karen: $x + 3$

Anna: $3x + 3$

Nina: $(x + 5) + 3 = x + 8$.

The sum of Karen and Nina’s age three years from now is $(x + 3) + (x + 8) = 2x + 11$. This is $4$ more than Anna’s age three years from now.  That means that if we add $4$ to Anna’s age, her age will equal the sum of the ages of the two girls. That is, $2x + 11 = 3x + 3 + 4$

This give us $2x + 11 = 3x + 7$ which gives us $x = 4$.

Therefore, Karen is $4$ years old, Anna is $12$, and Nina is $9$.