# Problem Solving: Find the age of the daughter

by Abdul

**Question**

If the age of a father is 2 times greater than his son and 3 times than his daughter, and their total age is 88. What is the age of daughter?

**Answer**

**STEP 1: **You are asked to find the age of the daughter. If you assume a variable for the daughter’s age, you will not be able to proceed any further with the calculations because no adequate information has been provided.

Choose a variable to represent the age of the father, say,

*f*. Since the relation the age of father has with the age of his son and daughter, and the total age are known, you can frame an equation.

**STEP 2: **The age of the father is two times that of his son. This implies that the son’s age is

^{f}/_{2} . Using the relation between the age of father and the age of daughter, you get her age as

^{f}/_{3}.

The three ages add up to 88.

Now we have an equation in terms of one variable that we can solve.

**STEP 3:** You see that the denominators of the fractions on the left are not the same. To be able to perform the addition, we need fractions with like denominators (

equivalent fractions). If we multiply the first fraction by

^{6}/

_{6}, the second by

^{3}/

_{3}, and the third by

^{2}/

_{2} , we can get equivalent fractions.

Now, simply add the numerators of the fractions writing the denominator only once.

**STEP 4: **Isolate the variable.

The age of the father is 48 years. But, you are asked to find the daughter’s age. Divide 48 by 3 for this purpose.

The age of the daughter is

**16 years**.