sara discarded 1/10 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 of the total apples picked were sold as fresh fruit?

Answer 1

Let \( x \) be the total number of apples that Sara picked.

First, she discarded \( \frac{1}{10} \) of the apples as defective. This means the number of defective apples is:

\[ \frac{1}{10} x \]

The number of apples that remained after discarding the defective ones is:

\[ x - \frac{1}{10} x = \frac{9}{10} x \]

Out of the remaining apples, 300 were made into cider. Thus, the number of apples remaining after making cider is:

\[ \frac{9}{10} x - 300 \]

This quantity is the number of apples sold as fresh fruit. We need to find out what fraction of the total apples picked were sold as fresh fruit.

The number of apples sold as fresh fruit is:

\[ \frac{9}{10} x - 300 \]

We will express the fraction of the fresh fruit sold out of the total apples picked, which is:

\[ \frac{\frac{9}{10} x - 300}{x} \]

To simplify this expression, we can break it down as follows:

\[ \frac{\frac{9}{10} x - 300}{x} = \frac{9}{10} - \frac{300}{x} \]

Now, we need to solve for \( x \) by considering that the number of remaining apples (after discarding the defective ones) must be at least 300, since she made cider from those:

\[ \frac{9}{10} x - 300 \geq 0 \]

Solving this inequality:

\[ \frac{9}{10} x \geq 300 \]

Multiplying both sides by \( \frac{10}{9} \):

\[ x \geq \frac{300 \times 10}{9} = \frac{3000}{9} \approx 333.33 \]

Since \( x \) must be a whole number, the minimum value for \( x \) is \( 334 \).

Now let’s calculate the fraction for the minimum case:

Substituting \( x = 334 \) into the expression for fresh fruit sold:

1. Find the total remaining apples: \[ \frac{9}{10} \times 334 = 300.6 \quad \text{(which rounds down to)} \quad 300 \] Therefore, if we consider that \( x = 334 \), \[ \text{Remaining apples} = 300 \]

However, since we know from the problem that 300 were made into cider, let's estimate \( x \) to find the apples sold fresh. This would require \( x = 400 \):

2. Then \( \text{remaining apples} = \frac{9}{10} x = \frac{9}{10} \cdot 400 = 360 \)
   • Cider = 300
   • Fresh fruits = \( 360 - 300 = 60 \)

Now we substitute for the fraction:

\[ \frac{60}{400} = \frac{3}{20} \]

Therefore, the fraction of the total apples picked that were sold as fresh fruit is:

\[ \boxed{\frac{3}{20}} \]