SOLUTION: In a speed typing test, each girl found that the girl sit on the left type twice as much as she type. The teacher note that each girl type a whole numbe rof lines and all the girls

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Question 555561: In a speed typing test, each girl found that the girl sit on the left type twice as much as she type. The teacher note that each girl type a whole numbe rof lines and all the girls typed 635 lines in total.
How many girl take the test?
Answer by KMST(5400) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of words typed by the girl on the right be a%5B1%5D.
The girl to her left typed a%5B2%5D=2a%5B1%5D words.
The next girl typed a%5B3%5D=2a%5B2%5D words, and so on.
The number of words typed by each girl, from right to left, forms a geometric sequence with common ratio 2.
The sum of the words typed by n girls is
S%5Bn%5D=a%5B1%5D%282%5En-1%29%2F%282-1%29=a%5B1%5D%282%5En-1%29
Since both factors must be integer,
635=5%2A127, and
5+1=6 is not a power of 2,
it must be a%5B1%5D=5 and
2%5En-1=127
So 2%5En=127%2B1=128=2%5E7 and n=7.