Question

Three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 33957. Find the

numbers.​

Answer 1

Given:

• Three numbers are in ratio 2:3:4.
• The sum of their cubes is 33957.

To Find:

• The three numbers.

Answer:

Let us take the given ratio be 2x:3x:4x .

Now , Sum of these numbers = 2x + 3x +4x = 9x.

Also , cube of these numbers

• (2x)³=8x³.
• (3x)³=27x³
• (4x)³=64x³.

Atq ,

=> 8x³+27x³+64x³=33957.

=> 99x³=33957

=> x³=33957/99

=>x³ = 343.

=> x = ³√343

=> x = 7.

Hence,

• First Number = 2x = 14.
• Second number = 3x = 21.
• Third Number = 4x = 28.

Answer 2

$\huge{\underline{\bigstar{\sf{solution!!}}}}$

The 3 numbers are : 0.3,0.45,0.6

⇛The question says there are three numbers but with a specific ration what that means in that once we pick one of the numbers the other two are know to us through the rations we can therefore replace all 3 of the numbers with a single variable:

2: 3: 4 ⇛ 2x × 3x × 4x

⇒now, no Matter what we chose for c we get the three numbers into the ratios specified we are also told the sum of the cubes of these three numbers which can write :

$({2x})^{3} + ({3x})^{3} + ({4x})^{3} = 0.334125$

⇛Disturbing the powers across the fact is using

$({a×b})^{c} = {a}^{c} {b}^{c} we\: get :$

${8x}^{3}+ {27x}^{3} + {64x}^{3} = {99x}^{3} = 0.334125$

${x}^{3} = \frac{0.334125}{99} = 0.003375$

${x}^{3} = \sqrt[3]{0.003375} = 0.15$

⇛So the 3 numbers are

$2×0.15, 3×0.15, 4×0.15$

$0.3,0.45,0.6$