Nikki is planting tomato plants in her garden. She has 20 feet along the back side where she plans to plant as many tomato plants as she can fit. The instructions specify to allow at least 20 inches between the holes where the plants will be planted. Assuming she wants all of the plants to be evenly spaced and that she plans to allow at least 10 inches between the plants on either side of the row and the fence on the sides, determine the number of plants she should buy. Also determine exactly where the plants should be planted to meet the conditions.
I honestly have no idea how to start on this .... 20 feet is 240 inches.. 10" on either side and 20" between plants
If I take 240" - 20" (2 x 10" for what is on the end), that leaves me with 220" for the plants, and that, divided by 20" is 11, so I could say she should buy 11 plants, but...that doesn't take into account how big the holes are.
And then, where to plant the plants....
from the left, at 10", 30", 50", 70", 90", 110", 130", 150", 170", 190", 210", 230"
That seems too easy and not correct?
To determine the number of plants Nikki should buy and their exact placement, let's break it down step by step:
Step 1: Calculate the available space for planting
- Nikki has 20 feet along the back side, which is equal to 240 inches.
- Considering the 10 inches required on either side of the row, subtract 20 inches from the available space.
- 240 - 20 = 220 inches of space for planting.
Step 2: Calculate the spacing between plants
- The instructions specify at least 20 inches between the holes where the plants will be planted.
- Since Nikki wants the plants to be evenly spaced, subtract 20 inches from the remaining available space.
- 220 - 20 = 200 inches.
Step 3: Determine the number of plants she should buy
- Divide the remaining available space by the spacing between plants to find the number of plants she can fit.
- 200 / 20 = 10 plants.
Step 4: Determine the exact placement of the plants
- Start from one end of the available space, leaving a 10-inch gap.
- Plant the first hole at 10 inches from the left.
- Continue planting the remaining holes at intervals of 20 inches.
- The exact placement of the holes would be: 10", 30", 50", 70", 90", 110", 130", 150", 170", and 190".
So, Nikki should buy 10 tomato plants and plant them at the following locations: 10", 30", 50", 70", 90", 110", 130", 150", 170", and 190".
To determine the number of plants Nikki should buy and their exact placement, let's break down the problem step by step:
1. Calculate the available space for planting: The back side of the garden is 20 feet or 240 inches long. Taking into account the 10 inches of space on either side for the fence, we can subtract 20 inches (2 x 10 inches) from the length, leaving us with 220 inches.
2. Calculate the required spacing between plants: Each tomato plant requires at least 20 inches of spacing between their holes. This means that the total space occupied by each plant, including the spacing, is 20 + 20 = 40 inches.
3. Divide the available space by the total space needed per plant: Divide the remaining space of 220 inches by the total space needed per plant (40 inches) to determine the number of plants Nikki can fit.
220 inches / 40 inches = 5.5
The result is 5.5, but since we can't have a fraction of a plant, we need to round down to the nearest whole number. Therefore, Nikki should buy 5 plants.
4. Determine the exact placement of the plants: To evenly space the plants, we can start by placing the first plant 10 inches from the left side of the garden. Then, we add 40 inches to each subsequent placement (20 inches for the plant and 20 inches for the spacing).
Plant #1: 10 inches from the left
Plant #2: 10 inches + 40 inches = 50 inches from the left
Plant #3: 50 inches + 40 inches = 90 inches from the left
Plant #4: 90 inches + 40 inches = 130 inches from the left
Plant #5: 130 inches + 40 inches = 170 inches from the left
Therefore, Nikki should buy 5 plants and place them at 10 inches, 50 inches, 90 inches, 130 inches, and 170 inches from the left side of the garden.