Question

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

Answer 1

Answer:

There are 150 blue marbles in Alex's bag.

Step-by-step explanation:

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

Initial ratio

$\frac{x}{y} = \frac{6}{10}$ (1)

$\frac{y}{z} = \frac{10}{15}$ (2)

Final ratio

$\frac{x + 10}{z - 25} = \frac{1}{2}$ (3)

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

$x - \frac{3}{5}\cdot y = 0$ (1)

$y - \frac{2}{3}\cdot z = 0$ (2)

$2\cdot (x + 10) = z - 25$

$2\cdot x +20 = z - 25$

$2\cdot x - z = -45$ (3)

The solution of the system of linear equations is:

$x = 90$, $y = 150$, $z = 225$

There are 150 blue marbles in Alex's bag.