Three numbers are in the ratio 2:3:4. The sum of their cubes is 334125. Find thenumbers
Question
Three numbers are in the ratio 2:3:4. The sum of their cubes is 334125. Find the numbers.
Solution
Let's denote the three numbers as 2x, 3x, and 4x.
The problem states that the sum of their cubes is 334125. So we can write the equation as follows:
(2x)^3 + (3x)^3 + (4x)^3 = 334125
Solving this equation will give us the value of x.
8x^3 + 27x^3 + 64x^3 = 334125
99x^3 = 334125
Divide both sides by 99 to isolate x^3:
x^3 = 334125 / 99
x^3 = 3375
Take the cube root of both sides to solve for x:
x = ∛3375
x = 15
Now that we have the value of x, we can find the three numbers:
2x = 215 = 30 3x = 315 = 45 4x = 4*15 = 60
So, the three numbers are 30, 45, and 60.
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