Three numbers are in the ratio 1:2:3. If the sum of the cubes of these numbers is 7776, then find the 3 no.s.
Answers
Answer:
The three numbers would be 6,12 and 18.
Step-by-step explanation:
First of all we know that all the three numbers are in ratio so we may take them as 1x , 2x , 3x respectively.
Now it is given that the sum of cubes of those numbers is 7776,so we will make an equation of sum of the above numbers(1x,2x and 3x). We will get,
=> ((1x)^3) + ((2x)^3) + ((3x)^3) = 7776
=> x^3 + 8(x^3) + 27(x^3) = 7776
=> 36(x^3) = 7776
=> x^3 = 7776/36
=> x^3 = 216
=> x = cube root of 216
=> x = 6
So x , 2x and 3x are equal to 6 , 12 and 18 respectively.
Now I will explain you about this in little more detail.
In these type of questions we generally take the numbers in the ratio with same variable like I took above(x , 2x and 3x). The trick to solve those questions is that we have to just make the equation and that we should know how to make. After we take the numbers in the ratio with the same variable we can refer to them as the original numbers so now we can approach according to the given question. In this question we took the "original" numbers(x , 2x and 3x) and cubed them as given in the question and also we wrote them in addition form as their sum was given(7776). So now with this much information we could easily take out the value of x and put in the value of "original" numbers x , 2x and 3x. So we get the original numbers as 6 , 12 and 18. The most important thing to be noted is that we took the same variable "x" in the ratio because whenever we cut(or divide) the numbers in ratio(or fraction) we always cut them with the number by which both(or many) numbers are divisible,we divide them with their common or same factors. Keeping this in mind we always is use the same variable with the numbers in the ratio.
Hope this helps you.
Answer:
hope it helps you friends
