Question

Three numbers are in the ratio 1 : 2 : 5. If the sum of their cubes is 3618, then the greatest number is

Answer 1

Three numbers are in the ratio 1 : 2 : 5. If the sum of their cubes is 3618, then the greatest number is 15

Solution:

Let the numbers be 1x, 2x and 5x. It is given that the sum of their cubes is 3618

Given that sum of their cubes is 3618

$(1 x)^{3}+(2 x)^{3}+(5 x)^{3}=3618$

$x^{3}+8 x^{3}+125 x^{3}=3618$

On solving we get,

$\begin{array}{l}{134 x^{3}=3618} \\\\ {x^{3}=\frac{3618}{134}} \\\\ {x^{3}=27} \\\\ {x^{3}=3^{3}} \\\\ {x=3}\end{array}$

Thus the numbers are:

1x = 1(3) = 3

2x = 2(3) = 6

5x = 5(3) = 15

Thus the greatest number is 15

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Answer 2

Given: Three numbers are in the ratio $1 : 2 : 5$ and if the sum of their cubes is $3618$.

To Find: What is the greatest number.

Step-by-step explanation:

Lets,

Take the three number are $x,2x\ and\ 5x$

If the sum of their cubes is $3618$.

∴ $x^{3}+(2x)^{3}+(5x)^{3}=3618$

⇒$x^{3}+8x^{3}+125x^{3}=3618$

⇒$x^{3}(1+8+125)=3618$

⇒$134x^{3}=3618$

⇒$x^{3}=\frac{3618}{134}$

⇒$x^{3}=27$

⇒$x^{3}=3^{3}$

∴ $x=3$

Therefore, All three number are,

First number is $3$

Second number is $(2\times 3)=6$

Third number is $(5\times 3)=15$

∴ The greatest number is $15$.