Question 1093381
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<pre>
Let x be the Grandfather age.


Then you have this equation from the condition

{{{x/7 + x/12 + (2/3)*x + 9}}} = x.


Multiply both sides by 7*12 = 84 to rid of denominators

12x + 7x + 56x + 9*84 = 84x,

75x + 9*84 = 84x,

9*84 = 84x - 75x  ====>  9*84 = 9x  ====>  x = 84.
</pre>

<U>Answer</U>.  Grandfather was 84 years old.



<pre>
          Notice that 7*12 = 84, therefore, one could suggest/guess the answer without calculations.
</pre>


To wider your horizon, there is very similar poetical mathematical legend from ancient times for the same theme and melody.


http://mathworld.wolfram.com/DiophantussRiddle.html




Also see these links in this forum


https://www.algebra.com/algebra/homework/word/age/Age_Word_Problems.faq.question.244899.html


https://www.algebra.com/algebra/homework/word/age/Age_Word_Problems.faq.question.427066.html