Question

A certain bag contains only red balls, green balls, and blue balls and no other balls. The ratio of the number of red balls to the number of blue balls is 2:3, and the ratio of the number of blue balls to the number of green balls is 4:3. The number of blue balls in the bag is what fraction of the total number of balls in the bag?
A. $\frac{3}{8}$
B. $\frac{12}{29}$
C. $\frac{7}{13}$
D. $\frac{15}{23}$
E. $\frac{12}{17}$

Answer 1

Answer:

Option B is right

Step-by-step explanation:

Given that a certain bag contains only red balls, green balls, and blue balls and no other balls. The ratio of the number of red balls to the number of blue balls is 2:3, and the ratio of the number of blue balls to the number of green balls is 4:3.

Red balls = 2x means blue balls = 3x

if blue balls = 3x then green balls would be = $\frac{3x(3)}{4} \\2.25x$

Now converting everything in terms of y we have

no of red balls = 2x, blue balls = 3x and green balls = 2.25x

Total balls = 7.25x

No of blue balls to total balls = $\frac{3x}{7.25x} \\=\frac{12}{29}$

Thus we find that option B is the only right answer