Question 1194346: Math
Encrypt the message “BYE” using the encryption e equals left parenthesis 5 m plus 9 right parenthesis m o d space 26. The table of number equivalents of the letters is given below.
Letter
Equivalent
A
0
B
1
C
2
D
3
E
4
F
5
G
6
H
7
I
8
J
9
K
10
L
11
M
12
N
13
O
14
P
15
Q
16
R
17
S
18
T
19
U
20
V
21
W
22
X
23
Y
24
Z
25
a) Change BYE into its numerical equivalent.
b) Find the encrypted number value for each.
c) Change back to letters.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Given Table:
| Letter | Numeric Equivalent | | A | 0 | | B | 1 | | C | 2 | | D | 3 | | E | 4 | | F | 5 | | G | 6 | | H | 7 | | I | 8 | | J | 9 | | K | 10 | | L | 11 | | M | 12 | | N | 13 | | O | 14 | | P | 15 | | Q | 16 | | R | 17 | | S | 18 | | T | 19 | | U | 20 | | V | 21 | | W | 22 | | X | 23 | | Y | 24 | | Z | 25 |
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Part (a)
From the table,
B = 1
Y = 24
E = 4
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Part (b)
Each number mentioned in part (a) will be plugged into the formula (5m+9) mod 26 to get the corresponding encrypted number.
For the letter B, we plug in m = 1
5m+9 = 5(1)+9 = 14
Mod this with 26 and we end up with 14, so no change happens.
In other words,
14/26 = 0 remainder 14
Therefore, the letter B gets encrypted to the number 14.
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For the letter Y, we plug in m = 24
5m+9 = 5(24)+9 = 129
Then we could say
129/26 = 4.96 approximately
So,
129 - 4*26 = 25
In short, 129/26 = 4 remainder 25
The letter Y gets encrypted to the number 25.
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For the letter E, we plug in m = 4
5m+9 = 5(4)+9 = 29
Then,
29 - 26 = 3
Therefore,
29/26 = 1 remainder 3
The letter E encrypts to 3.
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Summary:
B ---> 14
Y ---> 25
E ---> 3
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Part (c)
Use the results of the previous part.
B maps to 14, which corresponds to the letter "O". Use the table above.
Y maps to 25, which is the letter Z.
E maps to 3, which is the letter D.
B: remainder 14 ---> letter O
Y: remainder 25 ---> Z
E: remainder 3 ---> D
The message "BYE" encrypts to "OZD"
where that first item is the letter "O" and not the number zero.
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