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.

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)  

8

step-by-step explanation: