First, let x or any variable represent the number of paintings Kate initially has. After selling 12 of it, her paintings now becomes only x - 12. Then, she purchased 7 more making the number of her paintings become x - 12 + 7 = x - 5. This number tantamount to 21.
x - 5 = 21 ; x = 26
Thus, Kate initially had 26 paintings.
She would have $904. 275 + 812= 1087. 75 + 60 + 48= 183. 1087 - 183 = 904. Check the math to make sure, I did it in my head.
Set up the equation ... 60 + 40X = total charges... where X is the number of hours (8.5)
60 + 40(8.5) = ?
60 + 340 = ?
400 = total charges