Question

Three number are in the ratio 2: 3: 4 the sum of their cube is 33597. Find the number

Answer 1

Answer:

Given :-

• Three numbers are in the ratio of 2 : 3 : 4.
• The sum of their cubes is 33597.

To Find :-

• What is the numbers.

Solution :-

Let,

➲ First Number = 2a

➲ Second Number = 3a

➲ Third Number = 4a

According to the question,

◆ Sum of their cubes is 33597.

⇒ (2a)³ + (3a)³ + (4a)³ = 33597

⇒ 8a³ + 27a³ + 64a³ = 33597

⇒ 35a³ + 64a³ = 33597

⇒ 99a³ = 33597

⇒ a³ = 33597/99

⇒ a³ = 339.36

⇒ a = ∛339.36

⇒ a = 6.97

⇒ a ≈ 7

➠ a = 7

Hence, the required numbers are :

❒ First Number :

↦ First Number = 2a

↦ First Number = 2(7)

↦ First Number = 2 × 7

➦ First Number = 14

❒ Second Number :

↦ Second Number = 3a

↦ Second Number = 3(7)

↦ Second Number = 3 × 7

➦ Second Number = 21

❒ Third Number :

↦ Third Number = 4a

↦ Third Number = 4(7)

↦ Third Number = 4 × 7

➦ Third Number = 28

∴ The numbers are 14, 21 and 28.

Answer 2

Step-by-step explanation:

Answer:

Given :-

• Three numbers are in the ratio of 2 : 3 : 4.
• The sum of their cubes is 33597.

To Find :-

• The numbers.

Solution :-

Let,

➲ First Number = 2x

➲ Second Number = 3x

➲ Third Number = 4x

ATQ,

⏩Sum of their cubes is 33597.

➠ (2x)³ + (3x)³ + (4x)³ = 33597

➠ 8x³ + 27x³ + 64x³ = 33597

➠ 35x³ + 64x³ = 33597

➠ 99x³ = 33597

➠ x³ = 33597/99

➠ x³ = 339.36

➠ x = ∛339.36

➠ x = 6.97

➠ x ≈ 7

➠x = 7

Hence, the numbers are :

First Number :

↦ First Number = 2x

↦ First Number = 2 × 7

First Number = 14

Second Number :

↦ Second Number = 3x

↦ Second Number = 3 × 7

Second Number = 21

Third Number :

↦ Third Number = 4x

↦ Third Number = 4 × 7

Third Number = 28

∴ The numbers are 14, 21 and 28.