Question

Three number are in ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers

Answer 1

Let the numbers be 1k, 2k , and 3k respectively
Since the sum of their cubes is 4500,
(1k)³+(2k)³+(3k)³=4500
--> k³(36)= 4500
--> k = 5

Hence, the numbers are: 5,10 and 15 respectively

Answer 2

Three number are in ratio 1 : 2 : 3 and the sum of their cubes is 4500. Then the three numbers are 5, 10 and 15

Solution:

Given that three numbers are in ratio 1 : 2 : 3

Let the three numbers be 1x, 2x , 3x

To find: the numbers

Also given that sum of cubes of numbers is 4500. So we can frame a equation as:

sum of cubes of numbers = 4500

$(1x)^3 + (2x)^3 + (3x)^3 = 4500$

Let us solve the above expression for "x"

$x^3 + 8x^3 + 27x^3 = 4500\\\\36x^3 = 4500\\\\x^3 = \frac{4500}{36}\\\\x^3 = 125$

Taking cube root on both sides,

$\sqrt[3]{x^3} = \sqrt[3]{125} \\\\x = \sqrt[3]{5 \times 5 \times 5}\\\\x = 5$

Thus the three numbers are:

1x = 1(5) = 5

2x = 2(5) = 10

3x = 3(5) = 15

Thus the three numbers are 5, 10 and 15

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