This is not the first time this problem has cropped up.
The usual reason for having problems with this is going straight to coding without a plan such as pseudocode or even better a flow chart.
Try this pattern (untested - your job) where there is a downward cascade, and doing the printing at the end instead of repeating the cout's needlessly:
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char letter;
if(grade >= 89.5)
letter = 'A';
elseif (grade >= 79.5)
letter = 'B';
... etc etc
else
letter = 'F';