Question

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

Answer 1

Step-by-step explanation:

Let the numbers be 2n,3n,4n.

Sum of their cubes is 33957

(2n)³+(3n)³+(4n)³=33957

8n³+27n³+64n³=33957

99n³=33957

n³=33957/99

n³=343

Smallest number is (2n)³ or 8n³.

8n³=8×343=2744

Smallest number is 2744.

Answer 2

The 3 numbers are : 0.3,0.45,0.6

$\large{\underline{\bigstar{\explanation!!}}}}$

⇛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

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

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

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

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

⇛So the 3 numbers are

$2×0.15, 3×0.15, 4×0.15$

$0.3,0.45,0.6$