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?
+36916 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
+128475 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 !!!
