Thread: Isolating a variable in the numerator

One homework problem I have asks me to find what age added to a set of 15 ages, would lead to a mean of 54.94. The total of the 15 ages given minus the missing age = 828.

I am not sure if I did this right, but I set up the following equation to locate the X variable (the missing age in the line of ages).

828+x divided by 16 = 54.94 or (828 + X)/16 = 54.94

I seem to forget how to isolate the X variable. No matter what I do, it doesn't seem to work out. Perhaps I didn't even set it up correctly.

I would appreciate any help on this.

Originally Posted by Ian

One homework problem I have asks me to find what age added to a set of 15 ages, would lead to a mean of 54.94. The total of the 15 ages given minus the missing age = 828.

I am not sure if I did this right, but I set up the following equation to locate the X variable (the missing age in the line of ages).

828+x divided by 16 = 54.94 or (828 + X)/16 = 54.94

I seem to forget how to isolate the X variable. No matter what I do, it doesn't seem to work out. Perhaps I didn't even set it up correctly.

I would appreciate any help on this.

Call y the sum of the 15 given ages and x the new age.

Then


and



So this isn't as simple as setting up one equation in one unknown.

So take the second equation and solve for y.


and insert this into the first equation:


<-- Multiply both sides by 16









-Dan

Thank you. I appreciate you help. As a follow up, so I know for the future, why is it that we used dual variables instead of simply plugging in the sum of the original figures? What principle?

And thanks again. I will make up another problem for myself and reverse engineer your answer.

Originally Posted by Ian

Thank you. I appreciate you help. As a follow up, so I know for the future, why is it that we used dual variables instead of simply plugging in the sum of the original figures? What principle?

And thanks again. I will make up another problem for myself and reverse engineer your answer.

Originally Posted by Ian

The total of the 15 ages given minus the missing age = 828.


828+x divided by 16 = 54.94 or (828 + X)/16 = 54.94

I'm looking at this again and wondering if I took the above sentence correctly. Literally speaking your statement implies that (sum of 15 ages) - (missing age) = 828, which is why my solution involved two variables because we don't know what the sum of the 15 ages is.

However from your followup post and re-reading the question I am wondering if this was a typo. In your original post were you trying to say that the sum of the 15 ages is 828? If so then the equation you posted is correct:
<-- Multiply by 16





-Dan