Problem Solving

Sometimes we are going to meet questions that exercise our minds. We can but hope that similar questions will not be asked in the real eleven plus examinations.

Seven years ago a man was three times as old as his son was then. The father is 37 years old. How old is the son?

Ask your child, “What are you trying to find?”

Answer: “The age of the son.”

“What unit of time do you need?”

Answer: “Years.”

“Do you know any facts?”

Answer: “Yes, we know that the father is 37 years old now.”

“Do you know any more information?”

Answer: “Well the question did say that the seven years ago the father was three times as old as his son was then.”

We now come to your completely logical solution. This will astound your child. Your partner will look at you completely differently from now on. You will have proved to the world your intelligence and aptitude. (And so on and so forth!)

“Let the “x” years be the son’s age now.

Seven years ago he was (x – 7) years old.

Seven years ago his father was three times as old as this.

So we need 3(x – 7)

So now his father is 3(x – 7) + 7 years old.

So now we back in the realm of easy eleven plus work.

3(x – 7) + 7 = 37
3x – 21 + 7 = 37
3x – 14 = 37
3x = 51
x = 17

So the son must be 17 years old!

If your can apply this sort of reasoning to the more complicated eleven plus questions then the whole family will sleep easier at night.