Question

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

Answer 1

Answer:

14, 21 and 28

Step-by-step explanation:

Let those numbers are 2a, 3a and 4a.

In question,

= > sum of cubes of these numbers = 33957

= > (2a)³ + (3a)³ + (4a)³ = 33957

= > 8a³ + 27a³ + 64a³ = 33957

= > 99a³ = 33957

= > a³ = 33957/99

= > a³ = 343

= > a = 7

Hence the numbers are:

2a = 2(7) = 14

3a = 3(7) = 21

4a = 4(7) = 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

$2×0.15, 3×0.15, 4×0.15$

$0.3,0.45,0.6$