The number of candies each of the grandchild would get is 24, 18 and 16 candies respectively.
Given the following data:
To determine the number of candies each of the grandchild would get:
Note: The candies were distributed to the grandchildren inversely proportional to their ages.
Mathematically, this is given by this expression:
[tex]Candies \; \alpha\; \frac{1}{Age}[/tex] ≡ [tex]C = \frac{k}{A}[/tex]
Thus, the above expression is re-written for all the grandchildren as follows:
[tex]58 = \frac{k}{6} + \frac{k}{8}+\frac{k}{9}[/tex]
Lowest common multiple (LCM) of 6, 8 and 9 is 72.
[tex]58=\frac{12k +8k+9k}{72} \\\\58=\frac{29k}{72}\\\\29k =72 \times 58\\\\29k =4176\\\\k=\frac{4176}{299}[/tex]
k = 144.
For the first grandchild:
[tex]Candy = \frac{k}{6} \\\\Candy = \frac{144}{6}[/tex]
Candy = 24 candies.
For the second grandchild:
[tex]Candy = \frac{k}{6} \\\\Candy = \frac{144}{8}[/tex]
Candy = 18 candies.
For the third grandchild:
[tex]Candy = \frac{k}{6} \\\\Candy = \frac{144}{9}[/tex]
Candy = 16 candies.
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