You are here:

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.


All Answers

Answers by Expert:

Ask Experts


Scott A Wilson


Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.


I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

Documents at Boeing in assistance on the manufacturiing floor.

MS at math OSU in mathematics at OSU, 1986. BS at OSU in mathematical sciences (math, statistics, computer science), 1984.

Awards and Honors
Both my BS and MS degrees were given with honors.

Past/Present Clients
Students in a wide variety of areas since the 80's; over 1,000 of them have been in algebra.

©2017 All rights reserved.