Let the total number of apples picked be \( x \).
Since Sara discarded \( \frac{1}{10} \) of the apples as defective, the number of apples discarded is:
\[ \frac{x}{10} \]
The apples remaining after discarding the defective ones is:
\[ x - \frac{x}{10} = \frac{10x}{10} - \frac{x}{10} = \frac{9x}{10} \]
Out of the remaining apples, 300 were made into cider. Therefore, the number of apples sold as fresh fruit is:
\[ \frac{9x}{10} - 300 \]
Now, we need to find the fraction of the total apples picked that were sold as fresh fruit. The fraction is given by:
\[ \frac{\frac{9x}{10} - 300}{x} \]
Simplifying the expression:
\[ = \frac{9x}{10x} - \frac{300}{x} = \frac{9}{10} - \frac{300}{x} \]
To find \( x \), we set up the equation based on the number of apples that were turned into cider:
\[ \frac{9x}{10} - 300 = \text{number of apples sold as fresh fruit} \]
We will have to substitute a value for \( x \) to calculate \( \frac{300}{x} \) and find the fraction sold as fresh fruit.
Assuming the number of fresh apples (total minus defective) equals 300 plus the other amount sold, we need to find the total apples picked.
From our cider equation:
- \( \frac{9x}{10} = 300 + \text{selling fresh} \)
- Rearranging for \( 300 + \text{selling fresh} = \frac{9x}{10} \)
Substituting \( \frac{3000}{9} \), we find:
We can solve for \( x \):
\[ 300 = \frac{9x}{10} - \text{selling fresh} \] Let’s assume when \( x = 1000 \): \[ 9*1000/10 - 300 = 900 - 300 = 600. \] So, \( 600 \) apples were sold as fresh.
Now computing:
\[ \frac{600}{1000} = \frac{3}{5} \]
Thus, the fraction of the total apples picked that were sold as fresh fruit is:
\[ \frac{3}{5} \]
So, the answer is:
\(\frac{3}{5}\)
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