Muddled Money
Aishwarya Rai walks into a bank to cash out her cheque By mistake, the bank teller gives her dollar amount in change and her cent amount in dollars. On the way home she spends 5 cents, and then suddenly she notices that she has twice the amount of her cheque.
How much was her cheque amount?
The answer is 31.63.
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1 solution
The check was for dollars 31.63.
The bank teller gave her dollars 63.31 She spent .05, and then she had dollars 63.26, which is twice the check.
Let x be the dollars of the check, and y be the cent.
The check was for 100x + y cent He was given 100y + x cent
Also 100y + x - 5 = 2(100x + y) Expanding this out and rearranging, we find: 98y = 199x + 5
or 199x ≡ -5 (mod 98) or 98 2 x + 3x ≡ -5 (mod 98) 3x ≡ -5 ≡ 93 (mod 98) this quickly leads to x = 31