Both of these problems require the use of constant ratios.
8.
LM/QR = NK/SP
(4x+4)/48 = (7x-9)/60
(x+1)/12 = (7x-9)/60
12(7x--9) = 60(x+1)
84x - 108 = 60x + 60
24x = 168
x = 7
9.
YZ/SZ = RT/ST
(2x+2)/35 = (3x-7)/40
35(3x-7) = 40(2x+2)
105x - 245 = 80x + 80
25x = 325
x = 13