Question

Three numbers are in the ratio 2:3:4 the sum of their cube's is 33,957 find the number

Answer 1

$\bigstar\;\boxed{\bf SoluTion}}}}}$

➩ Let the numbers be 2x, 3x and 4x

➩ Sum of cubes = 33957

$\sf {\Rightarrow (2x)^{3} + (3x)^{3} + (4x)^{3} = 33957}\\\\\\\sf {\Rightarrow 8x^{3} + 27x^{3} + 64x^{3} = 33957}\\\\\\\sf {\Rightarrow 99x^{3} = 33957}\\\\\\\sf {\Rightarrow x^{3} = \frac{33957}{99} = 343}\\\\\\\sf {\Rightarrow x = \sqrt[3]{343}= 7}$

The numbers are :-

$\mapsto \boxed {\sf 2x = 2 \times 7 = 14}\\\\\\\mapsto \boxed {\sf 3x = 3 \times 7 = 21}\\\\\\\mapsto \boxed {\sf 4x = 4 \times 7 = 28}$