# What was the amount of the check?

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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.)

posted May 13, 2014

x=dollars, y=cents of original check
(100x+y)*3=100y+x-50
I used a spreadsheet to compute values of x for 1 to 100
The only integer that came out for y was 56.
\$56.18 - \$0.50 = \$55.68
\$55.68 / 3 = \$18.56

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A man went into a bank to cash a cheque. In handing over the money the cashier, by mistake, gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home.

He then found that he possessed exactly twice the amount of the cheque. He had no money in his pocket before going to the bank. What was the exact amount of that cheque?