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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
 #1
avatar+19832 
+2

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
 #2
avatar+104932 
+1

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

 

So

 

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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