168 Chapter 3 Solving Equations Group Activity Deciphering a Coded Message Materials: Pencil and paper Estimated Time: 20 minutes Group Size: Pairs Cryptography is the study of coding and decoding messages. One type of coding process assigns a number to each letter of the alphabet and to the space character. For example: A B C D E F G H I J K L M N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 O P Q R S T U V W X Y Z space 15 16 17 18 19 20 21 22 23 24 25 26 27 According to the number assigned to each letter, the message “Do the Math” would be coded as follows: D O _ T H E _ M A T H 4 / 15 / 27 / 20 / 8 / 5 / 27 / 13 / 1 / 20 / 8 Now suppose each letter is encoded by applying a formula such as x 3 y, where x is the original number of the letter and y is the code number of the letter. For example, the letter A would be coded by 1 3 4, B would be coded 2 3 5, and so on. Using this encoding, we have Message: D O _ T H E _ M A T H Original: 4 / 15 / 27 / 20 / 8 / 5 / 27 / 13 / 1 / 20 / 8 Coded form: 7 / 18 / 30 / 23 / 11 / 8 / 30 / 16 / 4 / 23 / 11 To decode this message, the receiver would need to reverse the operation by solving for x, that is, use the formula x y 3. 1. Each pair of students will encode the message by adding 3 to each number: Life is too short for long division. 2. Each pair of students will decode the message by subtracting 3 from each number. 17 / 4 / 23 / 24 / 21 / 4 / 15 / 30 / 17 / 24 / 16 / 5 / 8 / 21 / 22 / 30 / 4 / 21 / 8 / 30 / 10 / 18 / 18 / 7 / 30 / 9 / 18 / 21 / 30 / 28 / 18 / 24 / 21 / 30 / 11 / 8 / 4 / 15 / 23 / 11
miller_prealgebra_2e_ch1_3
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