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?

Guest Nov 7, 2019

#1**+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

ElectricPavlov Nov 7, 2019

#2**+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 !!!

CPhill Nov 8, 2019