The sum of the cubes of two numbers is 280. If these numbers are in the ratio 2 to 3, what is the smaller number?

Explanation

Let the two numbers be 2x and 3x. Their cubes sum to 280: (2x)³ + (3x)³ = 280, which simplifies to 8x³ + 27x³ = 280 or 35x³ = 280. Solving for x³ gives x³ = 8, so x = 2. Therefore, the smaller number is 2 × 2 = 4.