Luke made an elaborate code to remember the 10-digit combination to his bicycle lock. This is the code he came up with: F-G-E-D-

Question

3 years ago

10

Luke made an elaborate code to remember the 10-digit combination to his bicycle lock. This is the code he came up with: F-G-E-D-

A-K-B-J-C-H Each letter stands for a different digit (0-9). Study the clues below to figure out what digit is represented by each letter. When two letters are written together without an operation symbol, they represent a tens digit and a ones digit. F+F+F=D B÷ H = K J + A = CC
H+H = B. F×H= CK. D×F = KG G+B+E=D+A+C. A×H = KE J÷F=K F/J = H/B

What is the 10-digit combination to Luke's bicycle lock?

this is all the information I have.
please show work by either showing a picture of explaining it in text. Thank you

Mathematics

2 answers:

AlladinOne [14] · Answer 1 · 2022-12-05T23:58:55+03:00

9514 1404 393

Answer:

lock code: 3709528614

Step-by-step explanation:

Given:

3F = D
H×K = B
J+A = CC
H×2 = B
H×F = CK
D×F = KG
G +B +E =D +A+C
H×A = KE
K×F = J

Find:

single digit corresponding to each letter

Solution:

CC must be 11, because the sum of any pair of single digits cannot exceed 18. (C = 1).

K must be 2, because H×K = B = H×2. (K = 2)

The only single-digit products involving 3 are 3×1 = 3, 3×2 = 6, and 3×3 = 9. We know F is not 1 or 2, so for 3F = D we must have F = 3, D = 9. (F = 3)(D = 9)

CK = 12, so H×F = 3H = 12. This means H = 4. (H = 4)

2H = B, so B = 8. (B = 8)

D×F = KG. Using the values for D, F, K, we find 9×3 = 27. (G = 7)

K×F = J = 2×3. (J = 6)

At this point, the only unassigned digits are 0 and 5.

H×A = KE. Filling in known values, this is 4A = 20 +E. (A = 5)(E = 0)

The sum E+15 = A+10 can also be used to assign values to A and E.

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Then the letters corresponding to the digits 0-9 are ...

$\texttt{01234 56789}\\\texttt{ECKFH AJGBD}$