Let's solve the problem step by step.
1. Initial amount of apples:
Marco initially picked [tex]\(8 \frac{1}{2}\)[/tex] pounds of apples.
We can convert [tex]\(8 \frac{1}{2}\)[/tex] to an improper fraction:
[tex]\[
8 \frac{1}{2} = 8 + \frac{1}{2} = \frac{16}{2} + \frac{1}{2} = \frac{17}{2}
\][/tex]
2. Apples used to make a pie:
Marco used [tex]\(\frac{1}{4}\)[/tex] of the apples to make a pie. To find this amount:
[tex]\[
\frac{1}{4} \times \frac{17}{2} = \frac{17}{8}
\][/tex]
So, [tex]\( \frac{17}{8} \)[/tex] pounds of apples were used for the pie.
3. Apples used to make applesauce:
Marco then used [tex]\(3 \frac{1}{8}\)[/tex] pounds of apples to make applesauce.
We convert [tex]\(3 \frac{1}{8}\)[/tex] to an improper fraction:
[tex]\[
3 \frac{1}{8} = 3 + \frac{1}{8} = \frac{24}{8} + \frac{1}{8} = \frac{25}{8}
\][/tex]
Here, [tex]\(3 \frac{1}{8}\)[/tex] is equivalent to [tex]\( \frac{25}{8} \)[/tex] pounds.
4. Total apples used:
Now, let's calculate the total amount of apples used by adding both quantities:
[tex]\[
\frac{17}{8} + \frac{25}{8} = \frac{17 + 25}{8} = \frac{42}{8}
\][/tex]
Simplifying [tex]\( \frac{42}{8} \)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (2):
[tex]\[
\frac{42}{8} = \frac{21}{4}
\][/tex]
5. Amount of apples left:
Finally, we subtract the amount of apples used from the initial amount to find out how many pounds of apples Marco has left:
[tex]\[
\frac{17}{2} - \frac{21}{4}
\][/tex]
To perform this subtraction, we need a common denominator for the fractions. The least common multiple of 2 and 4 is 4. Convert [tex]\( \frac{17}{2} \)[/tex] to a fraction with a denominator of 4:
[tex]\[
\frac{17}{2} = \frac{34}{4}
\][/tex]
Now the subtraction:
[tex]\[
\frac{34}{4} - \frac{21}{4} = \frac{34 - 21}{4} = \frac{13}{4}
\][/tex]
Convert [tex]\( \frac{13}{4} \)[/tex] to a mixed number:
[tex]\[
\frac{13}{4} = 3 \frac{1}{4}
\][/tex]
Therefore, Marco has [tex]\(3 \frac{1}{4}\)[/tex] pounds of apples left. So the answer is:
[tex]\[
\boxed{3 \frac{1}{4}}
\][/tex]
