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bonanova

Question

It was his first day as bank teller, and Adam made a big mistake.

When Judy handed him a check for $AB.CD, the cash he gave her amounted to $CD.AB instead.

When Judy later bought a newspaper for $0.50, she realized the mistake.

She also counted her remaining money and found it was exactly 3 times the original amount of the check.

What was the value of the check?

That is, what are the values [not necessarily different] of A, B, C and D?

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56.18

My sketch:

cd.ab = 3 * ab.cd + .50

3a <= c <= 3a+2

b = 3d

When d is 1, 2, or 3

b is 3, 6, or 9

a = 3 * c + 5

No solution

When d is 4, 5, 6

b is 2, 5, 8

a = 3 * c + 6

c = 5 a = 1

56.18 = 3 * 18.56 + .5 (bingo!)

When d is 7, 8, 9

b is 1, 4, 7

a = 3 * c + 7

No feasible a, c pair

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