SOLUTION: 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

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(3816) (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

================================================
Part (a)

From the table,
B = 1
Y = 24
E = 4

================================================
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.

---------------

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.

---------------

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.

---------------

Summary:
B ---> 14
Y ---> 25
E ---> 3

================================================

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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