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?
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
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
1 not an tnteger
2 not an integer
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 !!!