## Lesson 7: Solution to Diophantus Riddle (VI)

March 17, 2012

This is the translation of the epitaph into Spanish:

” Aquí fueron sepultados los restos de Diofanto. La infancia de Diofanto duró 1/6 de su vida, 1/12 en la adolescencia, cuando la barba cubrió su cara, Después de 1/7 de su vida contrajo nupcias. Luego de cinco años de casado nació su primer hijo. El hijo vivió ½ de la vida de su padre, su padre buscó consuelo en los números pero no lo logró y murió cuatro años después que él.”

Let x be the age of Diophantus. If we translate the epitaph into Algebra:

x/6 +x/12 +x/7 +5 +x/2 +4 = x
14x/84 +7x/84 +12x/84 +420/84 +42x/84 +336/84= 84x
14x +7x +12x +420 +42x +336= 84x
14x +7x +12x +42x -84x= -420 -336
-9x = -756
x = -756/-9 =  84  years old.

Then we have that Diophantus was born about 200 and died about 284.

## Lesson 7: Linear and Quadratic Equations. Maths Are Magic (V)

March 5, 2012

### How old are you?

If you ask this to your great-aunt it would be indiscreet. So we are going to do it in other way …Play the following game

 Tell her:Think of a number between 1 and 9. Multiply it by 9. Take away this result from 10 times your age and tell me the answer.

Now you could guess your great-aunt’s age.

You will always get your great-aunt’s age. Is it Magic or Maths?

Why are we always right? Could you give a logic reason?