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Three numbers are in the ratio 2: 3: 5 . The sum of their cubes is 34560 . Find the numbers.
Given: Three numbers are in the ratio of 2 : 3 : 5
The sum of their cubes is 34560
To do: Find the numbers
Solution:
Lets assume the numbers are $2x,3x$ and $ 5x$
Sum of their cubes is 34560
$(2x)^3 + (3x)^3 + (5x)^3 = 34560$
$8x^3 + 27 x^3 + 125 x^3 = 34560$
$160 x ^3 = 34560$
$ x^3 = \frac{34560}{ 160}$
$x^3 = 216$
$ x^3 = 6 \times 6 \times 6$
$ x = 6$
Therefore, the numbers are
$2(6) , 3(6) , 5(6)$
12 , 18 , 30
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