Sara discarded I of the apples she picked as defective. Of the apples remaining, 300 were made into cider. The rest were sold as fresh fruit. What fraction of the total apples picked were sold as fresh fruit? (1 point)

1 answer

Let's denote the total number of apples Sara picked as \( x \).

Sara discarded \( \frac{1}{4} \) of the apples (assuming "I" means "1/4"). Therefore, the number of apples she discarded is:

\[ \frac{1}{4}x \]

The number of apples remaining after the discards is:

\[ x - \frac{1}{4}x = \frac{3}{4}x \]

From the remaining apples, 300 were made into cider. The rest of the remaining apples were sold as fresh fruit, which can be calculated as follows:

\[ \text{Apples sold as fresh fruit} = \left(\frac{3}{4}x - 300\right) \]

Now, we need to find the fraction of the total apples picked that were sold as fresh fruit:

\[ \text{Fraction of total apples sold as fresh fruit} = \frac{\frac{3}{4}x - 300}{x} \]

To simplify this fraction, we can separate the terms in the numerator:

\[ \frac{\frac{3}{4}x - 300}{x} = \frac{\frac{3}{4}x}{x} - \frac{300}{x} = \frac{3}{4} - \frac{300}{x} \]

Now, solving for \( x \) (the total number of apples picked) given that \( \frac{3}{4}x - 300 = 0 \) (i.e., when the remaining apples equals the cider made), we can rearrange:

\[ \frac{3}{4}x = 300 \]

Multiplying both sides by \( \frac{4}{3} \):

\[ x = 300 \times \frac{4}{3} = 400 \]

Now substitute \( x = 400 \) back into the equation for fresh fruit:

The total number of apples picked is 400, and the number sold as fresh fruit is calculated as follows:

\[ \text{Remaining apples} = \frac{3}{4} \times 400 = 300 \] \[ \text{Fresh fruit} = 300 - 300 = 0 \text{ (therefore this approach isn't correct here)} \]

However, we need the total number sold as fresh fruit:

\[ \frac{3}{4}x - 300 = \frac{3}{4} \cdot 400 - 300 = 300 - 300 = 0 \]

We can conclude instead the calculation for apples sold should mean \( 300 - 300\) was \( x \).

Therefore our overall fraction based only on final cider is \( 0 \).

Rather the final fraction \( \text{Selling Fresh Fruit} \):

Thus:

\[ \frac{\text{sold}}{total} = \frac{300}{400} = \frac{3}{4}

So the correct is

[ \boxed{0} \]