SOLUTION: The sum of the ages of a married couple and their four children is 40 years over the century mark. Ten years ago, the sum f the ages of the couple, the eldest child and the second

Question 464882: The sum of the ages of a married couple and their four children is 40 years over the century mark. Ten years ago, the sum f the ages of the couple, the eldest child and the second cild is 5 decades and 5 years less than the sum of all (the six of them) their ages now. The father�s age is 10 times the age of the youngest, while the mother�s age is 8 times that of the youngest. The difference between the age of the second cild and the sum of the ages of the third and the last child is zero, while the difference between the ages of the first child and the sum of the ages of the second and last child is also zero. How old is the father now?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let

represent the father's age. Let

represent the mothers age, and let

and

represent the ages of child 1, 2, 3, and 4.

The first thing we know is that:

(Eq 1)

The next thing we are told is something about the situation 10 years ago:

Which can be simplified to:

(Eq 2)

Then we are told that

(Eq 3)

and

(Eq 4)

and

(Eq 5)

and finally:

(Eq 6)

Notice the handy (and very necessary) fact that we have 6 equations to match our 6 variables.

Start by combining Equations 1 and 2. Multiply (2) by -1 and add the result to (1) with the following result: