## 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?

###### Freely translated from Matemágicas. Descartes Project

1. She thought the number 7.
I multiplied by 8, so it’s 56.
Now I substract 130 (ten times my age) minus 56 = 74.
Witten as an equation can be: x=7·8-(10·13)

• There is a mistake, you must multiply by 9 instead of 8. I will give you a clue: look at nine multiplication table, it is curious isn’t it?

2. monica it’s for you:

1.-Think a number of five figures, the first and the fifth can’t be equal.
2.-Change the first figure with the last one.(If you write 12345, now you must write 52341)
3.-Now subtract the smallest number to the bigger number.(52341 – 12345 = 39996)
4.-Change the first and the last figure and add it to the other number that tou get in the step number four.(69993 + 39996)
5.-The number is 109989.

• I will try it, I suppuse you will give me an extra point in my exam, but if you want some extra grade you have to solve my riddle about how to guess someone’s age.

3. Hello Monica I did´t understand this problem at all but I think the answer is 85, Because: first I thougth in the number five and i multiplyed it by 9, then I took away this result from 10 times my age (13), so after that I have x= 130-45=85
This can be express as : x=10·13-5·9 /// x=130-45 /// x=85

4. Let x be the great aunt´s age.
The number I thought was 7.
I am 13 years old.
FORMULA= (10·13) – (7·9) = 130 – 56 = 74 years old is the great aunt.

• The age you must always use is your great aunt’s age (never your age, you are too young to have problems to tell it!)

• You have to use your great-aunt’s age! Your age doesn’t matter.

5. Monica I think the problem it’s wrong because you don’t guess your great-aunt’s age, but I have other way to guess it:

tell her:
-Multiply the number 12345679 by 9.
-Finally take the first and the last numbers and you will have your great-aunt’s age.

6. The number is 7, so 7·9=63.
Now 14·10(ten times mi age) minus 63= 140-63=77 is the granma’s age.
Written as an equation can be:
x=(10·14)- 7·9

7. Hi Mónica.
My solution:
Let x be the great-aunt´s age, I thought the number 5 so if I multiply it by 9 it´s 45.
Now I substract 130, that is 10 times my age, by 45, that is 85. So my great-aunt´s age is 85.
Like a fraction it could be: x= 5 · 9 – (13·10)

• Mónica, when i wrote “like a fraction” is as an equation.
Bye

8. Monica we are Alba and Esther and we try to do it and we can ´t we never guess our great- aunt´ s age.