Thank you for visiting A park has a ginkgo tree a dogwood tree and two blue spruce trees The blue spruce trees are 8 years old The ginkgo tree. 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 :
Answer:
The age of the grinkgo tree is 10 years old and the age of the dogwood tree is 4 years old
Step-by-step explanation:
Let
x -----> the age of the grinkgo tree
y -----> the age of the dogwood tree
z -----> the age of the blue spruce tree
we know that
[tex]x=3y-2[/tex] ------> equation A
[tex]z=8[/tex] ----> equation B
[tex]x=\frac{1}{2}(y+2z)[/tex]
substitute the value of z
[tex]x=\frac{1}{2}(y+2(8))[/tex]
[tex]x=\frac{1}{2}(y+16)[/tex] -----> equation C
equate equation A and equation C and solve for y
[tex]3y-2=\frac{1}{2}(y+16)[/tex]
[tex]6y-4=(y+16)[/tex]
[tex]6y-y=16+4[/tex]
[tex]5y=20[/tex]
[tex]y=4[/tex]
Find the value of x (equation A or equation C)
[tex]x=3(4)-2=10[/tex]
therefore
The age of the grinkgo tree is 10 years old and the age of the dogwood tree is 4 years old
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Rewritten by : Jeany
Final answer:
To find the ages of the grinkgo and the dogwood trees, we need to solve the equation (x + 8 + 8) / 2 = 3x - 2, where x represents the age of the dogwood tree.
Explanation:
Let's assume the age of the dogwood tree is x years. According to the given information, the age of the blue spruce trees is 8 years. The grinkgo tree is 2 years less than three times the age of the dogwood tree, which can be written as 3x - 2. Additionally, the grinkgo tree is half the sum of the ages of the dogwood tree and both blue spruce trees, so its age is (x + 8 + 8) / 2. Therefore, we have the equation:
(x + 8 + 8) / 2 = 3x - 2
Solve this equation to find the age of the dogwood tree (x) and the grinkgo tree (3x - 2).
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