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Answer :
To solve the problem of finding out how many geraniums are needed for a circular garden with an outside circumference of 23 feet, where each geranium is planted every 6 inches around the garden, we follow these steps:
1. Understand the Problem: We have a circular garden with a known circumference, and we want to plant geraniums at regular intervals along the perimeter.
2. Convert Units: Since the distance between planting each geranium is given in inches, it's important to convert the circumference from feet to inches. Knowing that 1 foot equals 12 inches, we do the following conversion:
[tex]\[
\text{Circumference in inches} = 23 \text{ feet} \times 12 \text{ inches per foot} = 276 \text{ inches}
\][/tex]
3. Determine Planting Interval: Geraniums are to be planted every 6 inches. This means you divide the total circumference by the distance between each planting:
[tex]\[
\text{Number of geraniums} = \frac{\text{Circumference in inches}}{\text{Distance between geraniums}}
\][/tex]
Substituting in the values:
[tex]\[
\text{Number of geraniums} = \frac{276 \text{ inches}}{6 \text{ inches per geranium}} = 46
\][/tex]
Therefore, you will need to plant 46 geraniums to go around the entire circumference of the garden.
1. Understand the Problem: We have a circular garden with a known circumference, and we want to plant geraniums at regular intervals along the perimeter.
2. Convert Units: Since the distance between planting each geranium is given in inches, it's important to convert the circumference from feet to inches. Knowing that 1 foot equals 12 inches, we do the following conversion:
[tex]\[
\text{Circumference in inches} = 23 \text{ feet} \times 12 \text{ inches per foot} = 276 \text{ inches}
\][/tex]
3. Determine Planting Interval: Geraniums are to be planted every 6 inches. This means you divide the total circumference by the distance between each planting:
[tex]\[
\text{Number of geraniums} = \frac{\text{Circumference in inches}}{\text{Distance between geraniums}}
\][/tex]
Substituting in the values:
[tex]\[
\text{Number of geraniums} = \frac{276 \text{ inches}}{6 \text{ inches per geranium}} = 46
\][/tex]
Therefore, you will need to plant 46 geraniums to go around the entire circumference of the garden.
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