Question

I have a bag with yellow and blue marbles. The ratio of blue marbles to yellow marbles is 4:3. If I add 5 blue marbles and remove 3 yellow marbles, the ratio will be 7:3. How many blue marbles were in the bag before I added more?

a) 15
b) 20
c) 25
d) 30

Answer 1

(4x + 5)/(3x - 3) = 7/3

7(3x - 3) = 3(4x + 5)

21x - 21 = 12x + 15

9x = 36

x = 4

There were 4(4) = 16 blue marbles before the 5 blue marbles were added.

None of the choices are correct.

Answer 2

To find the original number of blue marbles in the bag, we first set up and solve a proportion based on the given ratios. After calculating the value of x, we determine that the bag initially contained 16 blue marbles, and the closest answer to this value is 15, option (a).

Step-by-step explanation:

To find the number of blue marbles in the bag before adding more, we need to set up a proportion based on the given ratios. Initially, the ratio of blue to yellow marbles is 4:3. Let's assume there are 4x blue marbles and 3x yellow marbles. After adding 5 blue marbles and removing 3 yellow marbles, the ratio changes to 7:3, which gives us the equation (4x + 5)/(3x - 3) = 7/3.

Now, solving for x in the equation:

• (4x + 5)/(3x - 3) = 7/3
• 12x + 15 = 21x - 21 (Cross-multiply)
• 15 + 21 = 21x - 12x (Move the terms involving x to one side and constants to the other)
• 36 = 9x (Combine like terms)
• x = 4 (Divide both sides by 9)

The number of blue marbles originally in the bag would be 4x, which means there were 4 * 4 = 16 blue marbles. Therefore, the closest answer from the given options is 15, which is choice (a).