Alex has a bag of marbles. Each marble is red, blue, or yellow , and the ratio of the red to blue to yellow marbles is 6:10:15. After Alex adds 10 red marbles and removes 25 yellow marbles form the bag, the ratio of red to blue to yellow is 2:3:4. How many blue marbles are in Alex's bag

There are 150 blue marbles in Alex's bag.

Step-by-step explanation:

Let , , be the quantities of red, blue and yellow marbles, respectively. From statement we derive three rational equations for initial and final ratios:

Initial ratio

(1)

(2)

Final ratio

(3)

After some algebraic handling we get the following system of linear equations:

(1)

(2)

(3)

The solution of the system of linear equations is:

, ,

There are 150 blue marbles in Alex's bag.

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw