Question

three no. are in ratio 2.3:4. the sum of their cube is, 33957 St.
find the no.​

Answer 1

Given:

Ratio of three numbers = 2:3:4

Sum of the cubes of the three numbers = 33,957

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To find:

The numbers

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Solution:

Let the first number be 2x.

Let the second number be 3x.

Let the third number be 4x.

Given that sum of their cubes is 33,957.

So,

$({2x})^{3} + ({3x})^{3} + ({4x})^{3} = 33957$

${8x}^{3} + {27x}^{3} + {64x}^{3} = 33957$

${99x}^{3} = 33957$

${x}^{3} = \dfrac{33957}{99}$

x³ = 343

$x = \sqrt{343}$

$\boxed {\boxed {\sf {\red {x=7}}}}$

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Final answer:

• First number = 2x

= 2×7

= 14

• Second number = 3x

= 3×7

= 21

• Third number= 4x

= 4×7

= 28

Therefore the three numbers are 14, 21 and 28.