# 3 numbers are in the ratio2:3:4.the sum of their cubes is 33957.find the number

Given: 3 numbers are in ratio 2: 3: 4

The sum of 3 numbers are = 33957

Let the first no. is 2x

Then the second and third no. would have been 3x and 4x respectively

According to the question,

2x + 3x + 4x = 9x = 33957

x = 33957/ 9

x = 3773

The numbers are as follows:

2x = 2* 3773 = 7546

3x = 3* 3773 = 11319

4x = 4* 3773 = 15092

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Let the cubes of numbers are 2x3, 3x3  and4x3

(2x)3+ (3x)3+ (4x)3= 33957

8x3 + 27 x 3+ 64x3= 33957

=> 99x3= 33957

=> x3=33957/99

= x3= 343

x=7

The numbers are

Ist numbe is 2x= 2*7=14

2nd number is 3x = 3*7 = 21

3rd number is 4x = 4*7 = 28

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Let the numbers be (2x)3:(3x)3:(4x)3
(2x)3+(3x)3+(4x)3= 33957
8x3+27x3+64x3= 33957
99x3= 33957
x3= 33957/99
x3=343
x=?343
x=7
The three numbers are=
2x=2?7=14
3x=3?7=21
4x=4?7=28
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2x+3x+4x=33957
9x=33957
X=33957/9
X=3773
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Let, first number is 2x
Second number is 3x
and third number is 4x

=> (2x )^3+(3x)^3+(4x)^3 = 33957
=> 8x^3 + 27x^3 + 64x ^3 = 33957
=> 99x^3 = 33957
=> x ^3 = 33957/99
=> x ^3=343
=> x =cube root 343
=> x = 7

Then the number will be
=> 2x = 2?7 = 14
=> 3x = 3?7= 21
=> 4x = 4?7= 28

Answer = The number are 14, 21, 28
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Find the square root of 135 424 in the steps
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By which smallest number must 5400 be multiplied to make it a perfect cube

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The ratio 2:3:4:5
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its answer is 92 to 15 evaluate the three numbers are in the ratio
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Let the numbers be 2x,3x,4x
According to the condition
(2x)^3+(3x)^3+(4x)^3=33957
8x^3+27x^3+64x^3=33957
99x^3=33957
x^3=33957?99
x^3=343
x=7
The numbers are
2x=2x7=14
3x=3x7=21
4x=4x7=28
The numbers are 14,21,28.
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