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Michelle asked her father how old he is. “Guess”, the father answered. “If you add the digits that make my age this year, you’ll get a number three times bigger than if you do it next year.” How old is the father?

Respuesta :

Maxvolcanos
He is 39 because 3+9=12, and next year he would be 40. 4+0=4, and 12 is 3 times larger than 4. He's old.
apocritia

Solution:

we are given that

“If you add the digits that make my age this year, you’ll get a number three times bigger than if you do it next year.”

Let the first digit of the father's age be x and the second digit be y

Then we can write

[tex]x+y= 3(x + y + 1) \\ \\ x+y= 3(x + y) + 3\\[/tex]

[tex]3(x+y)-(x+y)=-3\\ \\ 2(x+y)=-3\\ \\ (x+y)=-3/2\\ \\[/tex]

Since  [tex]x + y[/tex] cannot be negative, 

So we can again write

[tex]x + y = 3(x + 1 + y - 9) \\ \\ x+y= 3(x + y - 8) \\ \\ x+y= 3(x + y) - 24[/tex]

[tex]2(x+y)=24\\ \\ x+y=12\\[/tex]

Hence  age of the father is 39.

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