To answer your questions about Mr. Nelson's potting soil usage, we'll break this down into three parts as indicated.
Part A: Calculate how much potting soil Mr. Nelson used for each tomato plant.
Mr. Nelson used an entire bag of potting soil, which holds 80 quarts, to pot 15 tomato plants. Therefore, the amount of soil used for each tomato plant can be calculated as follows:
\[ \text{Soil used per tomato plant} = \frac{\text{Total soil used}}{\text{Number of tomato plants}} = \frac{80 \text{ quarts}}{15 \text{ plants}} = \frac{80}{15} = \frac{16}{3} \text{ quarts or } 5\frac{1}{3} \text{ quarts.} \]
Part B: What is the total amount of potting soil used with both the pepper and tomato plants?
We already have the amount of soil used for each type of plant:
- For the pepper plant: 3 2/3 quarts
- For the tomato plants: 80 quarts (for all 15 tomato plants)
Now, let's convert \(3\frac{2}{3}\) quarts into an improper fraction for easier calculations:
\[ 3\frac{2}{3} = \frac{11}{3} \text{ quarts.} \]
Now, we find the total amount of potting soil used for both:
\[ \text{Total potting soil used} = \text{Soil for tomatoes} + \text{Soil for pepper} = 80 + \frac{11}{3}. \]
To add these, we can convert 80 into a fraction:
\[ 80 = \frac{240}{3}. \]
Now we can add:
\[ \text{Total potting soil used} = \frac{240}{3} + \frac{11}{3} = \frac{240 + 11}{3} = \frac{251}{3} \text{ quarts or } 83\frac{2}{3} \text{ quarts.} \]
Part C: If Mr. Nelson wants to pot 6 more pepper plants with the same amount of soil (3 2/3 quarts each), will he have enough soil left from the bag after potting the 15 tomato plants and 1 pepper plant?
First, let’s calculate the total soil needed for the 6 additional pepper plants:
\[ \text{Soil needed for 6 pepper plants} = 6 \times 3\frac{2}{3} = 6 \times \frac{11}{3} = \frac{66}{3} = 22 \text{ quarts.} \]
Now, let’s see how much soil is left after potting the 15 tomato plants and 1 pepper plant:
Total soil used so far (from Part B) is \(80 + 3 \frac{2}{3} = \frac{240}{3} + \frac{11}{3} = \frac{251}{3}\).
Total soil in the bag is 80 quarts, or \(\frac{240}{3}\) quarts.
Now we calculate the soil left:
\[ \text{Soil left} = \text{Total soil in bag} - \text{Total soil used} = \frac{240}{3} - \frac{251}{3} = \frac{240 - 251}{3} = \frac{-11}{3}. \]
Since the result, \(\frac{-11}{3}\), is negative, it indicates that Mr. Nelson does not have enough soil to pot the 6 additional pepper plants after potting the tomatoes and the one pepper plant.
Thus, the answer to whether he has enough soil left is No.
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