Question

Three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 21,384. Find the numbers.

Answer 1

STEP-BY-STEP EXPLANATION:

.

Let's,

• The first number = 2x,
• The second number = 3x
• And, The third number = 4x.

According To Question,

The sum of the cube of the numbers is 21384.

As,

• ➺ (2x)³ + (3x)³ + (4x)³ = 21384
• ➺ 8x³ + 27x³ + 64x³ = 21384
• ➺ 99x³ = 21384
• ➺ x³ = 216
• ➺ x³ = 6³
• ➺ x = 6

The first number = 2(6) = 12

The second number = 3(6) = 18

And, The third number = 4(6) = 24

REQUIRED ANSWER,

• The numbers are 12, 18 and 24.

Answer 2

QuEsTiOn,

• Three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 21,384. Find the numbers.

To FiNd,

• $\color{red} \boxed{ \sf \: The \: numbers}$

SoLuTiOn,

• (2x)³ + (3x)³ + (4x)³ = 21384
• 8x³ + 27x³ + 64x³ = 21384
• 99x³ = 21384
• x³ = 216
• x³ = 6³
• x = 6

FiNaL AnSwEr,

$\color{orange} \boxed{ \sf \: The \: numbers \: are \: 12, 18 \: and \: 24}$

Hope you get your AnSwEr.