A memory card is one quarter full when 375 more pictures are taken it'll be two thirds full how many pictures can the memory card hold and how many pictures are on it?

x = what the card holds

1/4 x = what it has now.
1/4 x + 375 = 2/3 x
Solve for x = what the card hold.
2/3 x is what is on it

Let's solve this step-by-step:

Step 1: Initial State
The memory card is one quarter full, which means it is 25% full.

Step 2: Calculate the Current Capacity
If the memory card is one-quarter (25%) full, then we can calculate its current capacity by dividing 100% by 25%:
100% / 25% = 4

This means that the memory card can hold 4 times its current value.

Step 3: Calculate Additional Pictures
We know that when 375 more pictures are taken, the memory card will be two-thirds (66.67%) full. We can calculate the additional pictures required by subtracting 25% (current filling) from 66.67% (desired filling):
66.67% - 25% = 41.67%

Step 4: Calculate the Required Capacity
To calculate the required capacity, we divide this percentage by the current filling (25%):
41.67% / 25% = 1.6668

This means that the required capacity is 1.6668 times the current capacity.

Step 5: Calculate Total Capacity
Since we determined earlier that the memory card can hold 4 times its current value, we multiply the required capacity by the current capacity:
1.6668 * 4 = 6.6672

Step 6: Round to the Nearest Whole Number
To find the nearest whole number, we round down the value we obtained in step 5 (6.6672):
6.6672 ≈ 6

This means the memory card has a capacity of 6 times its current value.

Step 7: Calculate the Number of Pictures on the Memory Card
To determine the number of pictures currently on the memory card, we need to multiply the current filling (25%) by the capacity:
25% * 6 = 1.5

So, the memory card can hold 6 times its current value, which is equivalent to 1.5 pictures. However, it is not possible to have a fraction of a picture, so we round down to the nearest whole number, which means the memory card can hold 1 picture.

Therefore, the memory card can hold 1 picture and it currently has 1.5 pictures on it.

To find out how many pictures the memory card can hold and how many pictures are currently on it, we can use a system of equations based on the given information.

Let's assume the memory card can hold "x" pictures and it is currently holding "y" pictures.

According to the problem, the memory card is one quarter full when 375 more pictures are taken. This can be expressed as:

y + 375 = (1/4) * x

Additionally, it is mentioned that when 375 more pictures are taken, the memory card will be two thirds full. This can be expressed as:

y + 375 = (2/3) * x

Now, we have two equations:

y + 375 = (1/4) * x
y + 375 = (2/3) * x

To solve these equations, we need to eliminate one variable. Let's eliminate "y" by subtracting the second equation from the first equation:

[(1/4) * x - (2/3) * x] = [(2/3) * x - (1/4) * x]
[(1/4) * x - (2/3) * x] = [(8/12) * x - (3/12) * x]
[(1/4) * x - (2/3) * x] = (5/12) * x

Thus, we have:

- (5/12) * x = 375

To solve for "x", we can multiply both sides of the equation by -12/5 to isolate "x":

x = 375 * (-12/5)
x = -900

Since it doesn't make sense for the memory card to hold a negative number of pictures, we discard this solution.

Therefore, there is no valid solution for the number of pictures the memory card can hold. It seems there might be some inconsistency or error in the given information. Please double-check the problem statement or provide any additional information if available.