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 picked were sold as fresh fruit?
3/10
4/5
3/5
Let x be the total number of apples picked.
Sara discarded 1/10*x apples as defective.
The number of apples remaining is x - 1/10*x = 9/10*x.
Out of the remaining apples, 300 were made into cider, leaving 9/10*x - 300 apples remaining.
The remaining apples were sold as fresh fruit, so the fraction sold as fresh fruit is (9/10*x - 300) / (9/10*x).
This can be simplified to (9x/10 - 300) / (9x/10).
Dividing both the numerator and denominator by 9/10, we get (9x/10) / (9x/10) - 300 / (9x/10).
Simplifying further, we get 1 - 300 / (9x/10).
Simplifying the fraction 300 / (9x/10), we get 300 * (10/9x).
This can be simplified further to 1000 / 3x.
Therefore, the fraction sold as fresh fruit is 1 - 1000 / 3x.
Since the fraction sold as fresh fruit is asked for, and 1000 / 3x = 3/10, the fraction sold as fresh fruit is 1 - 3/10 = 10/10 - 3/10 = 7/10.
Thus, the fraction of the total apples picked that were sold as fresh fruit is 7/10.
Therefore, the answer is 7/10
To determine the fraction of the total apples picked that were sold as fresh fruit, we need to find the fraction of apples that remained after discarding 1/10 of them.
Let's assume Sara picked a total of x apples.
Then, the number of apples discarded as defective would be 1/10 * x = x/10.
The number of remaining apples would be x - x/10 = (10x - x)/10 = 9x/10.
Out of the remaining apples, 300 were made into cider. Therefore, the number of apples sold as fresh fruit would be (9x/10) - 300.
The fraction of apples sold as fresh fruit would be ((9x/10) - 300) / x.
Simplifying this expression, we get (9x - 3000) / 10x.
Since we are looking for a fraction, we can also write this expression as (9x/10x) - 3000/10x.
Simplifying further, we have 9/10 - 3000/10x.
Since we are looking for a fraction, the denominator should be the same. Therefore, we can multiply the second fraction by x/x to get a common denominator.
So the fraction of apples sold as fresh fruit is (9x/10x) - (3000/10x) = (9x - 3000)/10x.
The fraction of the total apples picked that were sold as fresh fruit is (9x - 3000)/10x.
Since the number of apples picked is not specified in the question, we cannot determine the exact fraction.
To find the fraction of the total apples picked that were sold as fresh fruit, we need to determine how many apples were left after Sara discarded 1/10 of the apples and made 300 into cider.
Let's assume that Sara picked x number of apples initially.
After discarding 1/10 of the apples, the number of remaining apples would be (1 - 1/10) times x, which simplifies to 9/10 times x.
Out of these remaining apples, 300 were made into cider. So, the number of apples left to be sold as fresh fruit would be (9/10 times x) - 300.
To find the fraction of the total apples picked that were sold as fresh fruit, we divide the number of apples sold as fresh fruit by the total number of apples picked:
[(9/10 times x) - 300] / x
Simplifying further:
(9/10 - 300/x)
Since we know the total number of apples picked, we can plug in a value for x and see which option is true.
Let's consider an example where Sara picked 1000 apples.
Using the equation above, we can calculate:
[(9/10 x 1000) - 300] / 1000 = (900 - 300) / 1000 = 600/1000 = 3/5
Therefore, in this case, 3/5 of the total apples picked were sold as fresh fruit.
So, the correct fraction of the total apples picked that were sold as fresh fruit is 3/5.