# Math problem

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Math problem

A friend of mine just sent me a rather funny brain teaser kind of math problem. The email alleges that this problem was included last year on one of the college tests of ITA in Brazil (Instituto Tecnológico de Aeronáutica). Here is the braintwister:

A mother is 21 years older than her son. In 6 years from now the mother will be 5 times older than the son. Question: Where is the father right now?

Answer (which is arrived at through pure mathematics):

The mother's age = Y years.

The son's age = X years.

Since the mother is 21 years older than the son, we have:

Y = X + 21

For X and Y, 6 years from now = (Y + 6) and (X + 6)

So if 6 years from now the mother will be 5 times older than the son, we have:

Y + 6 = 5(X + 6)

Working the equation a bit, we get:

Y + 6 = 5X + 30

Thus:

Y = 5X + 24

If we replace the above value for Y in the first equation (Y = X + 21), we get:

5X + 24 = X + 21

Working the equation further for a pure number value on one side, we get:

5X - 1X = 21 - 24

Thus:

4X = -3

This means:

X = -3/4

The son today is -3/4 year old. In other words, he is -9 meses old.

The original question was: Where is the father right now?

Answer: While you have been busting your brains trying to figure all this out, he is in bed right now with the mother having a grand old time!

Michael

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This is quicker.

E1: Y = X + 21

E2: Y + 6 = 5 (X + 6)

E2 - E1: 6 = 4X + 9

Transpose: 4X = -3

Divide: X = -3/4

Where is the father? Unknown.