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Hello,

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!

You can formulate a system of linear equations to solve this.

If we let the values of the individual letters be represented by the letter variable themselves,

then

B+ 2O + K = 13

F+ U+ 2L = 19

S + A + I + L = 20

B + O + I + L = 11

S + I + L + K= 18

F + O + I + L =10

The resulting augmented matrix can be written as such:

A B F I K L O S U

0 1 0 0 1 0 2 0 0 13

0 0 1 0 0 2 0 0 1 19

1 0 0 1 0 1 0 1 0 20

0 1 0 1 0 1 1 0 0 11

0 0 0 1 1 1 0 1 0 18

0 0 1 1 0 1 1 0 0 10

A first tier reduction of the matrix gives

A= 12 - 1/2 O - 1/2 S

B= 3 - 3/2 O + 1/2 S

F= 2 - 3/2 O + 1/2 S

I= -1/2 - 1/4 O - 1/4 S + 1/2 U

K= 10 - 1/2 O - 1/2 S

L= 17/2 + 3/4 O - 1/4 S - 1/2 U

O= O

S = S

U= U

Assuming all letters are associated with integer values, then a possible choice would be to let

Then

Naturally there will be many other possible solution sets since this system involves 9 variables yet is only described by 6 equations.

Hope this helps. Peace.

Algebra

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