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Sara has a bag which at the start contains 10 red marbles and 12 white marbles. When she draws out a red marble, she puts the marble back and adds five more red marbles. When she draws out a white marble, she puts the marble back and adds three more white marbles. What is the fewest number of rounds of draws/replacements/additions after which the bag could contain exactly 43 marbles?

 Nov 7, 2019

22 marbles to start    43 to finish     she must add 21 marbles


red   red   red   white   white  (inany order)       she will add 5  5  5  3  3 = 21 marbles in 5 draws

 Nov 7, 2019

Here's another way

Call  x  the number  of draws  in which 5 marbles  are added

Call  y   the number  of draws  in which  3  marbles  are added




5x +  3y  =  21


x     y

0    7

1    not an tnteger

2    not an integer

3    2

4    not an integer

5    y  is negative


We can stop  here


x + y   is minimized   when x  =  3  and y  = 2


So...as EP found.....5 draws  !!!



cool cool cool

 Nov 8, 2019

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