The memory card on Roger's digital camera hold z pictures(of equal size). After using up 1/4 of spaces on the memory card, Roger took 7 more pictures. The card then had 5/7 of its memory remaining. What is the value of z?

Would you subtract 5/7 from 1/4 and then divid by 7?

To find the value of z, we need to set up an equation using the given information.

Let's start by representing the total number of spaces on the memory card as x.

According to the question, after using up 1/4 of the spaces on the memory card, Roger took 7 more pictures. This means that 1/4 of the spaces were used, leaving 3/4 of the spaces available. So, the number of spaces available after using 1/4 of the spaces can be represented as (3/4)x.

Now, it is given that after taking 7 more pictures, the memory card had 5/7 of its memory remaining. This means that 5/7 of the spaces were available. So, the number of spaces available after taking 7 more pictures can be represented as (5/7)x.

Since the number of spaces available after using 1/4 of the spaces and the number of spaces available after taking 7 more pictures is the same, we can set up an equation:

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

To solve this equation, we can multiply both sides by 28 (the least common multiple of 4 and 7):

28 * (3/4)x = 28 * (5/7)x

21x = 20x

Now, subtracting 20x from both sides of the equation:

21x - 20x = 20x - 20x

x = 0

But wait! We cannot have 0 spaces on the memory card, which means there must be an error in the given information or the problem itself. Please double-check the values or the wording of the problem.

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