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I was given this problem, the answer was 4,200 USD but the explanation given to me on how it was solved was not clear. How do I solve this problem?

Teddy has a certain amount of pocket money for a 3 day vacation. On the first day, he spent 200 USD for breakfast and went shopping spending half of the money he had left. He then again spent 200 USD for dinner and went to bed. He did the same thing during the rest of his vacation and on the night of his last day, he went to bed with no more pocket money left. How much pocket money did he originally have?

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    $\begingroup$ Just work backwards. Teddy had $\$200$ before dinner on the third day, so he had $\$400$ before he went shopping the third day and $\$600$ before breakfast. Lather, rinse, repeat. $\endgroup$ – Robert Shore May 15 at 23:36
  • $\begingroup$ Thanks so much! $\endgroup$ – Jasper May 16 at 5:44
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$[((0+200)\cdot2+200+200)\cdot2+200+200]\cdot 2+200 = \$4200$

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