In a certain code language, the word "FRIED" is written as "EQHDC". Using the same letter-shift pattern, how is the word "RUSTY" written in that code language?

Introduction / Context: This is a letter-shifting coding–decoding question, sometimes called a Caesar cipher style problem. A given word is encoded by shifting each of its letters forward or backward by a fixed number of positions in the alphabet. Once you identify the shift used for one word, you apply it to a second word.

Given Data / Assumptions:

• "FRIED" is coded as "EQHDC".
• We must find the code for "RUSTY" using the same rule.
• The English alphabet is used with A as 1, B as 2, ..., Z as 26.
• The shift is uniform for all letters in the same word.

Concept / Approach: To discover the rule, we compare each letter of "FRIED" with its coded counterpart in "EQHDC". If each letter moves by the same number of positions, this is a simple Caesar shift. Once the shift is known, we apply it to each letter in the new word "RUSTY".

Step-by-Step Solution: Step 1: Map each letter of FRIED to EQHDC. F → E, R → Q, I → H, E → D, D → C. Step 2: Convert letters to positions and check the difference. F (6) → E (5): shift −1. R (18) → Q (17): shift −1. I (9) → H (8): shift −1. E (5) → D (4): shift −1. D (4) → C (3): shift −1. The same shift of −1 is applied to every letter. Step 3: Apply the same shift to RUSTY. R (18) − 1 = 17 → Q. U (21) − 1 = 20 → T. S (19) − 1 = 18 → R. T (20) − 1 = 19 → S. Y (25) − 1 = 24 → X. Step 4: Put the letters together: Q T R S X.

Verification / Alternative check: You can quickly re-encode "FRIED" using the −1 shift to confirm the rule. If any letter did not follow the same shift, you would need a different pattern, but here the shift is perfectly uniform.

Why Other Options Are Wrong: Other options correspond to different shifts or inconsistent letter changes. For instance, any answer that does not have Q for R or X for Y clearly does not use the same −1 pattern.

Common Pitfalls: One frequent mistake is to miscount letter positions or to shift in the wrong direction (for example, shifting +1 instead of −1). Writing the alphabet with numeric positions beside it helps avoid these errors.

Final Answer: According to the same coding rule, "RUSTY" is written as QTRSX.