To determine if Mr. Nelson can pot 17 pepper plants and have 17 2/3 quarts of potting soil left, we need to know how much potting soil he has in total and how much soil he needs for the pepper plants.
Let's denote:
- \( S \) as the total amount of potting soil Mr. Nelson has.
- \( P \) as the amount of potting soil required to pot 17 pepper plants.
- The amount of potting soil left after potting the plants will be \( S - P \).
Mr. Nelson wants to have 17 2/3 quarts left, which can be converted to an improper fraction for easier calculations: \[ 17 \frac{2}{3} = \frac{51}{3} + \frac{2}{3} = \frac{53}{3} \text{ quarts}. \]
For Mr. Nelson to successfully pot the plants and have 17 2/3 quarts left, the following inequality must hold: \[ S - P \geq \frac{53}{3}. \]
This means that Mr. Nelson needs to have enough potting soil in total ( \( S \) ) so that after potting the plants ( \( P \) ), the remaining soil ( \( S - P \) ) is at least \( \frac{53}{3} \).
Without the specific amount of potting soil Mr. Nelson starts with ( \( S \) ) and the amount needed for potting the 17 pepper plants ( \( P \) ), we cannot definitively state whether he can achieve his goal.
In conclusion, to determine if it is possible for Mr. Nelson to pot the plants and still have the required amount of soil left, we need to know:
- The total amount of potting soil he has ( \( S \) ).
- The amount of potting soil needed per pepper plant, and thus the total for 17 plants ( \( P \)).
If \( S \) is indeed greater than or equal to \( P + \frac{53}{3} \), then yes, it is possible. If not, then it is not possible.
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