Let the total number of apples picked be \( x \).
First, Sara discarded \( \frac{1}{10} \) of the apples, which means the number of defective apples is:
\[ \frac{1}{10}x \]
The number of apples remaining after discarding the defective ones is:
\[ x - \frac{1}{10}x = \frac{9}{10}x \]
From the remaining apples, 300 were made into cider. Therefore, the number of apples left that were sold as fresh fruit can be calculated as:
\[ \frac{9}{10}x - 300 \]
To find what fraction of the total apples picked \( x \) were sold as fresh fruit, we need to find the number of fresh fruit apples in relation to \( x \):
\[ \text{Fraction sold as fresh fruit} = \frac{\frac{9}{10}x - 300}{x} \]
Simplifying the fraction gives:
\[ \frac{\frac{9}{10}x - 300}{x} = \frac{9}{10} - \frac{300}{x} \]
At this point, we need to analyze the option choices to find possible values of \( x \).
Let’s set \( \frac{9}{10}x - 300 \geq 0 \) to ensure there are fresh apples to sell:
\[ \frac{9}{10}x \geq 300 \] \[ x \geq \frac{300 \times 10}{9} = \frac{3000}{9} \approx 333.33 \]
Now, consider the lowest integer value, \( x = 334 \):
Calculating for \( x = 334 \):
\[ \frac{9}{10} \cdot 334 = 300.6 \quad (\text{so approximately 300 apples to cider}) \] \[ \frac{9}{10} \cdot 334 - 300 = 300.6 - 300 = 0.6 \quad (\text{not realistic since it yields a non-integer}) \]
Let’s try \( x = 400 \):
Calculating for \( x = 400 \):
\[ \frac{9}{10} \cdot 400 = 360 \] \[ \frac{9}{10} \cdot 400 - 300 = 360 - 300 = 60 \]
Calculating the fraction of apples sold as fresh fruit:
\[ \frac{60}{400} = \frac{3}{20} \]
Since \( \frac{3}{20} \) isn't an option, Let's now continue until \( x = 500 \):
For \( x = 500 \):
Calculating for \( x = 500 \):
\[ \frac{9}{10} \cdot 500 = 450 \] \[ \frac{9}{10} \cdot 500 - 300 = 450 - 300 = 150 \]
Calculating the fraction of apples sold as fresh fruit:
\[ \frac{150}{500} = \frac{3}{10} \]
That matches one of our options! Hence, the fraction of total apples picked that were sold as fresh fruit is:
B. \( \frac{3}{10} \)
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