Multiple choice general knowledge math & puzzles

A confused bank teller transposed the dollars and cents when he cashed a check for Ms Smith, giving her dollars instead of cents and cents instead of dollars. After buying a newspaper for 50 cents, Ms Smith noticed that she had left exactly three times as much as the original check. What was the amount of the check? (Note: 1 dollar = 100 cents.)

  1. $28.26
  2. $18.56
  3. $19.87
  4. $12.00
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the check be D dollars and C cents. The teller gave C dollars and D cents, which is 100C + D cents total. After spending 50 cents, she has 100C + D - 50 = 3(100D + C). Solving: 100C + D - 50 = 300D + 3C, which gives 97C - 299D = 50. The unique valid solution is C=18, D=56, giving $18.56. This is a classic Diophantine equation problem.

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