Lending Money to Darlene

Franklin lent Darlene as much money as she already had, then she spent $10. The next day, Franklin lent her as much money as she now had and again, she spent $10. On the third day Franklin once again lent her as much money as she now had and she spent $10, leaving her broke. How much money did Darlene start with?

You may have been tempted to guess $30 because $10 is spent three times, but that would mean she would have had $60 ($30 lent plus the $30 she already had), and $50 after spending $10. The rest of the numbers end up at higher than zero, so we know it has to be less than $30. Even starting at $10 leaves Darlene with $10 on the third day. Starting with $8.75 works out as follows.

Day 1: $8.75 (lent) + $8.75 (already had) – $10 (spent) = $7.50 (remaining)
Day 2: $7.50 + $7.50 – $10 = $5
Day 3: $5 + $5 – $10 = $0

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