Thank you for visiting Part A A park has a ginkgo tree a dogwood tree and 2 blue spruce trees The blue spruce trees are 8 years old The. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Let's tackle this problem step by step!
### Part A
We need to find an equation that relates the ages of the ginkgo tree and the dogwood tree. Let's break down the information given:
1. The park has a ginkgo tree, a dogwood tree, and 2 blue spruce trees.
2. Each blue spruce tree is 8 years old.
3. The age of the ginkgo tree is the same as the age of the dogwood tree. Additionally, the ginkgo tree's age is also half the sum of the ages of the dogwood tree and both blue spruce trees.
Given:
- Let [tex]\( d \)[/tex] be the age of the dogwood tree.
- The age of each blue spruce tree is 8 years, so both together are [tex]\( 8 + 8 = 16 \)[/tex] years.
According to the problem statement, the ginkgo tree is half the sum of the ages of the dogwood tree and both blue spruce trees:
- [tex]\( \text{Ginkgo tree's age} = \frac{1}{2} \times (\text{Dogwood tree's age} + 16) \)[/tex]
- This translates to the equation: [tex]\(\text{Ginkgo tree's age} = \frac{1}{2}(d + 16)\)[/tex].
Additionally, we know the age of the ginkgo tree is also equal to that of the dogwood tree. Thus, the ginkgo tree's age can be written as [tex]\( \frac{1}{2}(d + 16) = \frac{1}{2}d + 8\)[/tex].
Combine this information to find a match with one of the given options:
- C) [tex]\(\frac{3}{2} d = \frac{1}{2}(d + 8 + 8)\)[/tex]
Thus, the correct equation is:
[tex]\[\frac{3}{2} d = \frac{1}{2}(d + 16)\][/tex]
### Part B
Now, let's solve this equation to find the ages of the trees.
1. Start with the equation from part A:
[tex]\[\frac{3}{2} d = \frac{1}{2}(d + 16)\][/tex]
2. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the right side:
[tex]\[\frac{3}{2} d = \frac{1}{2}d + 8\][/tex]
3. Subtract [tex]\(\frac{1}{2}d\)[/tex] from both sides to isolate [tex]\( d \)[/tex]:
[tex]\[\frac{3}{2}d - \frac{1}{2}d = 8\][/tex]
4. Simplify the left side:
[tex]\[d = 8\][/tex]
Therefore, the dogwood tree is 8 years old.
5. Now, find the age of the ginkgo tree using its relation to the dogwood tree:
[tex]\[\text{Ginkgo tree's age} = \frac{1}{2} (d + 16) = \frac{1}{2} (8 + 16) = \frac{1}{2} \times 24 = 12\][/tex]
The ginkgo tree is 12 years old.
So, the ginkgo tree is 12 years old, and the dogwood tree is 8 years old.
### Part A
We need to find an equation that relates the ages of the ginkgo tree and the dogwood tree. Let's break down the information given:
1. The park has a ginkgo tree, a dogwood tree, and 2 blue spruce trees.
2. Each blue spruce tree is 8 years old.
3. The age of the ginkgo tree is the same as the age of the dogwood tree. Additionally, the ginkgo tree's age is also half the sum of the ages of the dogwood tree and both blue spruce trees.
Given:
- Let [tex]\( d \)[/tex] be the age of the dogwood tree.
- The age of each blue spruce tree is 8 years, so both together are [tex]\( 8 + 8 = 16 \)[/tex] years.
According to the problem statement, the ginkgo tree is half the sum of the ages of the dogwood tree and both blue spruce trees:
- [tex]\( \text{Ginkgo tree's age} = \frac{1}{2} \times (\text{Dogwood tree's age} + 16) \)[/tex]
- This translates to the equation: [tex]\(\text{Ginkgo tree's age} = \frac{1}{2}(d + 16)\)[/tex].
Additionally, we know the age of the ginkgo tree is also equal to that of the dogwood tree. Thus, the ginkgo tree's age can be written as [tex]\( \frac{1}{2}(d + 16) = \frac{1}{2}d + 8\)[/tex].
Combine this information to find a match with one of the given options:
- C) [tex]\(\frac{3}{2} d = \frac{1}{2}(d + 8 + 8)\)[/tex]
Thus, the correct equation is:
[tex]\[\frac{3}{2} d = \frac{1}{2}(d + 16)\][/tex]
### Part B
Now, let's solve this equation to find the ages of the trees.
1. Start with the equation from part A:
[tex]\[\frac{3}{2} d = \frac{1}{2}(d + 16)\][/tex]
2. Distribute the [tex]\(\frac{1}{2}\)[/tex] on the right side:
[tex]\[\frac{3}{2} d = \frac{1}{2}d + 8\][/tex]
3. Subtract [tex]\(\frac{1}{2}d\)[/tex] from both sides to isolate [tex]\( d \)[/tex]:
[tex]\[\frac{3}{2}d - \frac{1}{2}d = 8\][/tex]
4. Simplify the left side:
[tex]\[d = 8\][/tex]
Therefore, the dogwood tree is 8 years old.
5. Now, find the age of the ginkgo tree using its relation to the dogwood tree:
[tex]\[\text{Ginkgo tree's age} = \frac{1}{2} (d + 16) = \frac{1}{2} (8 + 16) = \frac{1}{2} \times 24 = 12\][/tex]
The ginkgo tree is 12 years old.
So, the ginkgo tree is 12 years old, and the dogwood tree is 8 years old.
Thank you for reading the article Part A A park has a ginkgo tree a dogwood tree and 2 blue spruce trees The blue spruce trees are 8 years old The. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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