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.

age problem 2

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. 

Checking the Answer

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.

age problem

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.

Checking the Answer

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.

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