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A car salesman sells 1 car on his first day, 2 cars on his second day, 4 cars on his third day, and so on, so that every day after the first, he sells twice as many cars as the day before. How many days does it take him to sell a total of at least 1000 cars?

Sagot :

reinhard10158

Answer:

10

Step-by-step explanation:

every day he doubles the number of sold cars compared to the previous day.

so the sequence goes along the powers of 2 :

1

2

4

8

16

32

64

128

256

512

1024 - so, latest here, of course, at least 1000 cars were sold. that would be day 11.

but - maybe we reached the total of 1000 cars already before that.

as you can see, the number of cars sold on a day is 1 bigger than the sum of cars sold on all previous days.

e.g. 8 = 4 + 2 + 1 + 1

64 ÷ 32 + 16 + 8 + 4 + 2 + 1. + 1

therefore, 1024 is bigger by 1 than the sum of the cars Sikhs before that day. so, that sum is 1023 and bigger than 1000.

so, with the 512 cars sold on day 10 he reached and surpassed the total 1000 sold cars mark.

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