Question

Three numbers are in the ratio 2 : 3 : 4. If the sum of their cubes is 50688, find the numbers

Answer 1

Answer:

Let the three numbers be

• 2x
• 3x
• 4x

Sum of their cubes -

• 50688

According to the Question -

→ (2x)³ + (3x)³ + (4x)³ = 50688

→ (8x)³ + (27x)³ + (64x)³ = 50688

→ 99x³ = 50688

→ x³ = 50688/99

→ x³ = 512

→ x = 8

Now, by putting the value of x as 8.

• 2x = 2×8 = 16
• 3x = 3×8 = 24
• 4x = 4×8 = 32

Therefore, the three numbers are 16,24 and 32.

Answer 2

Answer:

So the numbers are

2x = 16

3x = 24

4x = 32

Step-by-step explanation:

Let the first number be 2x

Second will be 3x

and third will be 4x

So making their cubes

8x^3 + 27x^3 + 64 x^3 = 50688

99x^3 = 50688

x^3 = 50688 ÷ 99

= 512

x = cuberoot 512

= 8

So the numbers are

2x = 16

3x = 24

4x = 32