A Confused Bank Teller

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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

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Let x be the number of dollars in the check, and y be the number of cents.

Then 100y+x-50 = 3(100x+y).

97y-299x = 50.

Therefore y = (50+299x)/97 where X and Y both need to be integers

Look for integer solutions of this equation.

When X=18, Y=56.

The original check amount was $18.56, the teller gave her $56.18 instead. After the newspaper, she had $55.68 which is 3 times $18.56

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