To determine whether Mr. Nelson can pot 17 pepper plants and still have 17 2/3 quarts of potting soil left, we need to calculate the total amount of potting soil he will need for the pepper plants and then check if this is less than the amount he has after accounting for the soil he wants to have left.
-
Calculate the total amount of potting soil needed for the pepper plants: Each pepper plant requires 3 2/3 quarts of soil. Since there are 17 plants, we will multiply:
\[ \text{Total soil for plants} = 17 \times 3 \frac{2}{3} \]
First, convert \(3 \frac{2}{3}\) to an improper fraction:
\[ 3 \frac{2}{3} = \frac{11}{3} \]
Now we perform the multiplication:
\[ 17 \times \frac{11}{3} = \frac{17 \times 11}{3} = \frac{187}{3} \text{ quarts} \]
-
Calculate the total amount of potting soil Mr. Nelson needs to have: He wants to have 17 2/3 quarts left after potting the pepper plants, which we also convert to an improper fraction:
\[ 17 \frac{2}{3} = \frac{53}{3} \text{ quarts} \]
-
Determine the total amount of potting soil Mr. Nelson needs in total (for the plants plus for himself): He will need the amount for the plants plus the amount he wants to have left:
\[ \text{Total soil needed} = \frac{187}{3} + \frac{53}{3} = \frac{187 + 53}{3} = \frac{240}{3} = 80 \text{ quarts} \]
-
Conclude whether Mr. Nelson can meet his requirements: If Mr. Nelson has a full bag of potting soil with a maximum capacity of less than 80 quarts, then he cannot satisfy his requirement. However, if he has 80 quarts or more, then it is possible.
In summary, whether Mr. Nelson can fulfill his need depends exactly on how much potting soil is in the full bag he has initially. If the bag contains at least 80 quarts, he can pot the peppers and have the specified amount left. If it contains less than this amount, it is not possible.
2 answers