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Algebra/Need help!


My math teacher gave us a worksheet with six 4-letter words.
Book = 13
Full= 19
Sail= 20
Boil = 11
Silk = 18
Foil = 10
Each letter in the word has a value and they all should equal the number after the word.
also, the B for instance in the word Book has to be the same value as the B in the word Boil, and etc.
I cannot figure this out after hours of trying. How do I do this? Thank you for your time!

I took the letters B, F, A, K, S, and O as non-zero values.
The rest of the letters are taken to have 0.
This generates a matrix
A   B   F   K   O   S   Equal to
0   1   0   1   2   0   13
0   0   1   0   0   0   19
1   0   0   0   0   1   20
0   1   0   0   1   0   11
0   0   0   1   0   1   18
0   0   1   0   1   0   10

The results were after solving are
B  20
F  19
A  13
K  11
S  7
O  -9

I checked back with the words, and they worked.
Since I picked I, L, and U to be zero to start with, this means this is only one possibility.
This implies that there could be up to 83 other possibilities.  After reviewing the problem,
I'm not sure all of them would be possible.  For example, if both F and B are left out, the letters in BOIL and FOIL would both reduce to OIL as the active letters, but the two words have different values.


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Scott A Wilson


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