Question

Three numbers are to one another 2 : 3 : 4. The sum of their cubes is 0.334125. Find the numbers.

Answer 1

Ratio in three numbers = 2 : 3 : 4
Let first number = 2x
Second number = 3x
and third number = 4x
$\therefore (2x{)}^3+(3x{)}^3+(4x{)}^3=0.334125\Rightarrow 8x^2+27x^3+64x^3=\frac{334125}{1000000}\Rightarrow 99x^3=\frac{334125}{1000000}\Rightarrow x^3=\frac{334125}{1000000\times 99}\Rightarrow x^3=\frac{3375}{1000000}$

$=\frac{3\times 3\times 3\times 5\times 5\times 5}{100\times 100\times 100}=\frac{3^3\times 5^3}{{100}^3}x=3\sqrt{\frac{3^3\times 5^3}{{100}^3}}=\frac{3\times 5}{100}=\frac{15}{100}=0.15$
$\therefore$ First number $=2x=2\times 0.15=0.30$
Second number $=3x=3\times 0.15=0.45$
Third number $=4x=4\times 0.15=0.60$
$\therefore$ Numbers are 0.3 , 0.45, 0.6