Question

Three numbers are in the ratio 3 is to 4 is to 5. The sum of their cubes is 157464. Find the numbers.

Answer 1

Answer:

Let the numbers be 3k,4k,5k

27k^3 +64k^3 +125k^3 =157464

216k^3 =157464

(6k)^3 =(54) ^3

6k=54

K=9

Therefore the numbers are 27,36,45

Answer 2

Answer:

First number is 27

Second number is 36

Third number is 45

Step-by-step explanation:

Let,

First number = 3x

Second number = 4x

Third number = 5x

The sum of their cubes is 157464

⇒ 27x³ + 64x³ + 125x³ = 157464

⇒ 216x³ = 157464

⇒ x³ = 157464 / 216

⇒ x³ = 729

⇒ $x \: = \: \sqrt[3]{729} \: = \: 9$

⇒ x = 9

★ First number = 3x

⇒ 3 (9)

⇒ 3 × 9

⇒ 27

★ Second number = 4x

⇒ 4 (9)

⇒ 4 × 9

⇒ 36

★ Third number = 5x

⇒ 5 (9)

⇒ 5 × 9

⇒ 45

Therefore,

First number is 27

Second number is 36

Third number is 45