Let's solve the problem step by step.

1. Identify the total amount of dried fruit: Let the total number of dried fruit pieces be $x$.

2. Determine the number of cherry pieces: Carina had 1/4 of the dried fruit as cherries, so the number of cherry pieces is: $\text{Number of cherries} = \frac{1}{4}x$

3. Calculate the remainder after removing cherries: After removing the cherries, the remaining dried fruit pieces are: $\text{Remaining fruit} = x - \frac{1}{4}x = \frac{3}{4}x$

4. Determine the number of pear pieces: 2/3 of the remaining fruit is pears, so: $\text{Number of pears} = \frac{2}{3} \times \frac{3}{4}x = \frac{1}{2}x$ We are told there are 48 pear pieces, so: $\frac{1}{2}x = 48$

5. Solve for $x$: $x = 48 \times 2 = 96$ So, the total number of dried fruit pieces is 96.

6. Determine the number of apple pieces: The number of cherry pieces is $\frac{1}{4}x = \frac{1}{4} \times 96 = 24$. The number of pear pieces is 48. The number of apple pieces is the remainder after subtracting the cherries and pears from the total: $\text{Number of apples} = x - 24 - 48 = 96 - 72 = 24$

So, there are 24 apple pieces.

Would you like any more details or have any questions about this solution?

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Here are 5 related questions:

1. What if 1/3 of the dried fruit was cherries instead of 1/4? How many apple pieces would there be then?
2. How many cherries would there be if the total number of dried fruit pieces was doubled?
3. What percentage of the dried fruit pieces are apples?
4. If Carina added 12 more pear pieces to the bag, what would be the new total number of fruit pieces?
5. If 3/5 of the apples were eaten, how many apples would remain?

Tip: When dealing with fractions of a total, it's often easier to first calculate the number of items for the given fractions before solving for the remainder.