The average age of a family consisting of two parents and their children is 20

If we exclude one parent who is 40 the average age drops to 15?

How many children are in the family?

Can you figure it out? Give this problem a try and when you're ready keep watching the video for the solution.

So while this is a straightforward algebra problem many people do not get the correct answer.

Some people incorrectly solve for the total number of people in the family and forget to exclude the two parents,

and other people do not set up the equations correctly because they forget there are two parents to calculate.

So we are going to solve this problem, and make sure we solve for the total number of children

We'll set a variable c to equal what we want: the number of children in the family.

We'll then denote a variable s to equal the sum of everyone's ages.

This is the sum of the two parents' ages plus the sum of all the children.

Now let's translate the word information into equations. We have the average age of the family equal to 20.

Now this numerator will be the sum of everyone's ages s.

The denominator will be the two parents plus the children.

So this will be c plus 2 and we want s divided by c plus 2 to equal the average 20.

The next condition is if we exclude one parent age 40 the average drops to 15.

So from this fraction,

we're going to remove 40 from the numerator and we're going to remove one observation - one individual - from the denominator

So we get s minus 40

divided by c plus 1, equals the average of 15.

So we now have a system of equations which we can solve.

We'll solve each equation for the variable s.

We now have two expressions for the variable 's' so we can set these two expressions equal to each other

We can now solve this equation for the single variable c.

We get the answer that c equals 3; there are three children in this family

Did you figure it out?

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