Question

Three numbers are in the ratio of 1:3:5 if the sum of their cubes is 4131 then find the number

Answer 1

Need to FinD :-

• The three numbers .

$\red{\frak{Given}}\begin{cases}\textsf{ Three numbers are in the ratio of 1:3:5 .}\\\\\textsf{ The sum of their cubes is 4131.}\end{cases}$

Given that the numbers are in ratio of 1:3:5 . And the sum of their cubes is 4131. So ,

Let us take ,

$\sf\longrightarrow Ratio = 1x : 3x : 5x$

Therefore ,

$\sf\longrightarrow Sum_{(of\ cubes)}=4131\\\\\\\sf\longrightarrow (1x)^3+(3x)^3+(5x)^3 =4131\\\\\\\sf\longrightarrow 1x^3+27x^3+125x^3=4131 \\\\\\\sf\longrightarrow 153x^3=4131\\\\\\\sf\longrightarrow x^3 = \dfrac{4131}{153} \\\\\\\sf\longrightarrow x^3 = 27\\\\\\\sf\longrightarrow x=\sqrt[3]{27} \\\\\\\sf\longrightarrow \underline{\underline{\red{\sf x = 3 }}}$

The Numbers ,

$\sf\longrightarrow \textsf{\textbf{ First number = x =\red{ 3} }}\\\\\\\sf\longrightarrow\textsf{\textbf{ Second number =3x = \red{ 9}}} \\\\\\\sf\longrightarrow\textsf{\textbf{ Third number = 5x = \red{15} }}$

Answer 2

${ \bold{ \underline{ \underline {\quad{Given :}{\quad}}}}}$

• Three numbers are in the ratio of 1:3:5 if the sum of their cubes is 4131. Find the numbers

${ \bold{ \underline{ \underline {\quad{Solution :}{\quad}}}}}$

• So, Let's consider the numbers as x , 3x and 5x where x is the constant of proportional.

$\tt{ {⇢}} \: (x)^3+(3x)^3+(5x)^3 =4131\\ \\ \\ \tt⇢ x^3+27x^3+125x^3=4131 \\ \\ \\ \tt⇢ 153x^3=4131 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt ⇢ \: x^3 = \dfrac{4131}{153} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt⇢ x^3 = 27 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt⇢ x=\sqrt[3]{27} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ ⇢{ \underline{ \boxed{ \frak{ \pmb{ \purple{ x =3}}}}}} \: \: \bigstar\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

⠀⠀⠀⠀⠀__________________

•⠀⠀First number = x = 3

•⠀⠀Second Number = 3x

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ = 3 × 3 = 9

•⠀⠀⠀Third Number = 5x

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 3 × 5 = 15

Hence, the required numbers are 3, 9 and 15