Answer:
There are 150 blue marbles in Alex's bag.
Step-by-step explanation:
Let [tex]x[/tex], [tex]y[/tex], [tex]z[/tex] be the quantities of red, blue and yellow marbles, respectively. From statement we derive three rational equations for initial and final ratios:
Initial ratio
[tex]\frac{x}{y} = \frac{6}{10}[/tex] (1)
[tex]\frac{y}{z} = \frac{10}{15}[/tex] (2)
Final ratio
[tex]\frac{x + 10}{z - 25} = \frac{1}{2}[/tex] (3)
After some algebraic handling we get the following system of linear equations:
[tex]x - \frac{3}{5}\cdot y = 0[/tex] (1)
[tex]y - \frac{2}{3}\cdot z = 0[/tex] (2)
[tex]2\cdot (x + 10) = z - 25[/tex]
[tex]2\cdot x +20 = z - 25[/tex]
[tex]2\cdot x - z = -45[/tex] (3)
The solution of the system of linear equations is:
[tex]x = 90[/tex], [tex]y = 150[/tex], [tex]z = 225[/tex]
There are 150 blue marbles in Alex's bag.
