+193 The letters of the alphabet are each assigned a random integer value, and $H=10$. The value of a word comes from the sum of its letters' values. If $MATH$ is 35 points, $TEAM$ is 42 points and $MEET$ is 38 points, what is the value of $A$?
+129852 M + A + T + 10 = 35 → M + A + T = 25 (1)
T + E + A + M = 42 (2)
M + E + E + T = 38 (3)
If we look at (1) and (2) we note that
T + E + A + M = 42
So
(M + A + T) + E = 42
So
25 + E = 42
E = 17
Looking at (3) we have that
M + E + E + T = 38
M + 2(17) + T = 38
M + T = 38 - 2(17)
M + T = 38 - 34
M + T = 4
So...looking back at (1)
M + A + T =25
M + T + A = 25
4 + A =25
A = 21
