36 - 47 = HAWAII - IOWA = HAI - O = -11

OHIO - (HAI - O) = OOO - A = 76
Thus, O=26, A=2 (since max vlue of letter is 26).

68 - 51 = ARKANSAS - KANSAS = AR = 2 + R = 17
Thus R=15

60 - 65 = IDAHO - OHIO = AD - O = -5 = 2 + D - 26
Thus, D=19

70 = NEVADA = NEV + 23
Thus, NEV=47

118 = VERMONT = NEV + R + O + MT = 47 + 15 + 26 + MT
Thus, MT=30

92 = MONTANA = MT + O + AA + NN = 30 + 26 + 4 + NN
Thus, NN=32; so N=16

79 = INDIANA = AA + D + II + NN = 4 + 19 + II + 32
Thus, II=24, so I=12

112 = FLORIDA = FL + O + R + I + D + A = FL + 26 + 15 + 12 + 19 + 2
Thus, FL=38

129 = CALIFORNIA = C + FL + AA + II + R + N + O = C + 38 + 4 + 24 + 15 + 16 + 26
Thus, C=6

140 = COLORADO = L + C + A + D + R + OOO = L + 6 + 2 + 19 + 15 + 78
Thus, L=20

38 = FL = F + L = F + 20
Thus, F=18

65 = OHIO = H + I + OO = H + 12 + 52
Thus, H=1

122 = ILLINOIS = S + III + LL + N + O = S + 36 + 40 + 16 + 26
Thus, S=4

178 = NORTHCAROLINA = T + AA + C + H + I + L + NN + OO + RR
Thus, T=21

27 = UTAH = U + T + A + H
Thus, U=3

85 = MISSOURI = M + I + I + O + U + R + S + S
Thus, M=9

53 = MAINE = E + M + A + I + N
Thus, E=14

46 = TEXAS = X + A + T + E + S
Thus, X=5

86 = ARIZONA = Z + AA + I + N + O + R
Thus, Z=13

47 = IOWA = W + I + O + A
Thus, W=7

51 = KANSAS = K + AA + N + SS
Thus, K=23

70 = NEVADA = V + AA + D + E + N
Thus, V=17

91 = MARYLAND = Y + AA + D + L + M + N + R
Thus, Y=8

116 = NEWJERSEY = J + EEE + N + R + S + W + Y
Thus, J=24

47 = ALABAMA = B + AAAA + L + M
Thus, B=10

91 = GEORGIA = GG + A + E + I + O + R
Thus, GG=22, so G=11

123 = MISSISSIPPI = PP + IIII + M + SSSS
Thus, PP=50, P=25

Thus, Q=22 (by pigeon-hole principle)