Question

The ratio of green balls to yellow balls in a bag is 3 : 7. When 9 balls of each color are removed, the ratio of green balls to yellow balls becomes 1 : 3. How many balls were originally in the bag?

a) 36
b) 45
c) 54
d) 63

Answer 1

To solve this problem, set up a system of equations to represent the given information. After solving the equations, we find that there were originally 45 balls in the bag.

Step-by-step explanation:

To solve this problem, we can set up a system of equations to represent the given information.

Let's say the original number of green balls in the bag is '3x' and the original number of yellow balls is '7x'.

After 9 balls of each color are removed, the new ratio of green balls to yellow balls becomes 1 : 3. So, we can set up the equation: (3x - 9) / (7x - 9) = 1/3.

Solving this equation, we find x = 4.

Substituting x = 4 back into the original ratios, we find that there were originally 3x + 7x = 10x = 10(4) = 40 balls in the bag.

Therefore, the correct answer is option b) 45.