I asked this question before, and got an answer, but I have a question about the response that was given. The original question was: For an initial investment of 100, an investment yields returns of X...

I asked this question before, and got an answer, but I have a question about the response that was given.  The original question was:

For an initial investment of 100, an investment yields returns of X₁ and X₂, where X₁ and X₂are independent normal random variables with mean 60 and variance 25.  What is the probability that the rate of return of this investment is greater than 10%?

In the answer that was given it says that the gain of the investment is X₁+X₂.  My question is why can we just group those together as one amount?  I was given a formula in my class that says the return on the investment would be the solution to the equation: -100+  X₁/(1+r) +   X₂/(1+r)²=0.  If this formula is used, a different solution would result for this problem.