This is the third part of the Solving Age Problems of the Math Word Problem Solving Series. In this post, we discuss more complicated age word problems.

**Problem 7**

Anna who is years old and his father Ben who is years old have the same birthday. In how many years will Ben be twice as old as Anna?

**Solution**

As years go by, the number of years added to Ben’s and Anna’s ages is the same. If we let the number of years that have gone by be , then in years, their ages will be

Ben’s Age:

Anna’s Age:

Since in years, Ben will be as twice as old as Anna, if we multiply Anna’s age by , their ages will be equal. So, we can now set up the equation

.

Solving, we have . which means that .

That means that in years, Ben will be twice as old as Anna.

**Checking the Answer**

In years, Ben will be years old. In years, Anna will be years old. Clearly, Ben will be twice as old as Anna in years, so we are correct.

**Problem 8**

The sum of the ages of James and Clark is . Five years ago, Clark’s age was three times as James’ age. How old are James and Clark now?

**Solution**

If James is years old, then Clark is years old (Why?). Five years ago, their ages were

James’ age:

Clark’s age: .

Since years ago, Clark’s age was three times as that of James, if we multiply James’ age by , their ages will be equal. So, we set up the equation

Solving we have, . This means that and . Therefore, James is years old and Clark is years old.

**Checking the Answer**

The sum of James age which is and Clark’s age which is is equal to . Five years ago, James was years old and Clark was . As we can see, Clark was three times as old as James. Therefore, we are correct.

**Problem 9***

Pol is years younger than Greg. In years, he will be years more than one half as old as Greg. Find their age at present.

**Solution**

Let be Greg’s age and let be Pol’s age. In 7 years, their ages will be

Greg’s age:

Pol’s age: .

In the problem, it is said that in years, Paul’s age will be ten years more than half of Greg’s age. Now, in years, half of Greg’s age will be

.

Now, since Paul is 10 more than one half Greg’s age, if we add years to half Greg’s age which is , their ages will be equal. Therefore,

.

Multiplying both sides by we have . Simplifying, we have which gives us . Therefore, Greg is years old and Pol is .

**Checking the Answer**

Greg is and Paul is , so Pol is years younger. In years, their ages will be and respectively. Half of Greg’s age by then is and if we add , the result is which equal’s Pol’s age.

**Sourc*e: http://algebra-word-problems.blogspot.com/2010/10/age-problem-5.html