Rule #1 Name Stuff.
What shall we name?
"how much money does she have in each account?"
F = Amount at 5%
S = Amount at 7%
E = Amount at 8%
This first step is VERY important. Do not get sloppy or careless. The more formal and deliberate you are right here, the easier the rest will go.
"She has three times as much invested at 8% as she does at 5%."
3F = E <== You must see the relationship between the words and this equation.
"If the total amount she has invested is $1600"
F + S + E = $1600 <== Do you see this one? Right out of the words.
"her interest for the year comes to $115,"
F(0.05) + S(0.07) + E(0.08) = $115 <== Again, right out of the words.
Reminder: You CANNOT get equations out of words without CLEAR definitions. That first step was just so important. I cannot sufficiently stress it.