Ken had a number of colored marbles in a bag. 1/4 of the marbles were red, 2/3 of the remaining marbles were blue, and the rest were yellow. Given that there were 120 red and yellow marbles altogether, how many marbles were there in the bag?

Well, well, well, we have a colorful problem here! Let's see if we can solve it with a splash of humor.

First, we know that 1/4 of the marbles were red. So, if we call the total number of marbles "x," we can say that (1/4) * x = 120.

Now, let's subtract those red marbles from the whole bunch. We'll have 3/4 of the marbles remaining.

Next, we're told that 2/3 of those remaining marbles were blue. So, (2/3) * (3/4) * x = 120.

Now, yellows are left. We already know that red and yellow marbles altogether make 120. So, if we subtract those from the total number of marbles, we'll find the number of yellow marbles.

We can say that x - (120 + 120) = number of yellow marbles.

And what's left after we have the yellows? The answer, my friend, is the total number of marbles in the bag!

Now, let me crunch some numbers and calculate the answer for you... Drumroll, please! 🥁

It seems like there were 480 marbles in the bag! Ta-da! Quite a colorful collection, I must say.

Let's begin solving the problem step-by-step:

Step 1: Determine the number of red marbles.
Given that 1/4 of the marbles were red, we can calculate the number of red marbles using the equation 1/4 * Total number of marbles = 120.
Rearrange the equation to solve for the total number of marbles: Total number of marbles = 120 / (1/4).

120 / (1/4) = 120 * (4/1) = 480

So, there were 480 red marbles.

Step 2: Determine the number of blue marbles.
Since 2/3 of the remaining marbles were blue, we subtract the number of red marbles (480) from the total number of marbles to find the remaining quantity: Total number of marbles - Red marbles = Remaining marbles.
Remaining marbles = 480 - 120 = 360.

Then, calculate the number of blue marbles using the equation (2/3) * Remaining marbles = Number of blue marbles.

(2/3) * 360 = 240

So, there were 240 blue marbles.

Step 3: Determine the number of yellow marbles.
Given that the red and yellow marbles altogether were 120, we can subtract the number of red marbles (480) from this total to find the number of yellow marbles: Total of red and yellow marbles - Red marbles = Yellow marbles.
Yellow marbles = 120 - 480 = -360.

So, there were -360 yellow marbles. However, this result does not make sense in the context of the problem. It is likely that there is an error or inconsistency in the information provided, as we cannot have a negative number of marbles.

Please check the problem statement again or provide additional information if available.

To solve this problem, we need to work step by step.

Let's start by figuring out the number of red marbles. We are told that 1/4 of the marbles were red. So, if we let "x" represent the total number of marbles in the bag, we can set up the equation: 1/4 * x = 120.

To solve for x, we need to multiply both sides of the equation by 4: 1/4 * x * 4 = 120 * 4.

Simplifying, we get: x = 480.

Now we know there are 480 marbles in total, and we need to find the number of yellow marbles. We are told that the total number of red and yellow marbles is 120, so we can subtract the number of red marbles from the total: 480 - 120 = 360.

So, there are 360 yellow marbles.

Finally, we need to find the number of blue marbles. We are told that 2/3 of the remaining marbles (after removing the red and yellow marbles) were blue. So we multiply the number of remaining marbles (360) by 2/3: 360 * 2/3 = 240.

Therefore, there are 240 blue marbles.

Adding up the number of red, yellow, and blue marbles, we get: 120 (red) + 360 (yellow) + 240 (blue) = 720.

Hence, there are 720 marbles in the bag.

red = .25

blue = 2/3 * .75 = .5
yellow = .25

I think you can take it from there