x= number of roses
x+4= number of geraniums
$5x + $3(x+4)= $52
multiply 3 by parentheses
5x + 3x + 12= 52
combine like terms
8x + 12= 52
subtract 12 from both sides
8x= 40
divide both sides by 8
x= 5 roses
CHECK
$5x + $3(x+4)= $52
(5*5) + 3(5+4)= 52
25 + 3(9)= 52
25 + 27= 52
52= 52
ANSWER: She bought 5 roses.
Hope this helps! :)