Question

The sum of the cubes of two numbers is 35. The numbers are in the ratio of 2:3. Find the numbers. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

Let the numbers be 2x and 3x since they are in the ratio of 2:3. Now their cubes have the sum of 35. This means $8x^3+27x^3=35$

$\Rightarrow 35x^3=35$

$\Rightarrow x^3=1$

$\Rightarrow x=1$

$\Rightarrow$ so the numbers are 2 and 3