Thank you for visiting A park has a ginkgo tree a dogwood tree and 2 blue spruce trees Write and solve an equation to find the ages of 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 :
Final answer:
To find the ages of the ginkgo and dogwood trees, we can write and solve an equation. The dogwood tree is 4 years old, while the ginkgo tree is 10 years old.
Explanation:
To find the ages of the ginkgo and dogwood trees, let's assign variables to represent their ages. Let's say the age of the dogwood tree is 'x'. The ginkgo tree's age will then be 2 years less than three times the age of the dogwood tree, so it is equal to 3x - 2. Moreover, the ginkgo tree's age is also half the sum of the ages of the dogwood tree and both blue spruce trees. Since the blue spruce trees are 8 years old, their sum is 8 + 8 = 16. Thus, we can write the equation as follows:
3x - 2 = (x + 16) / 2.
- To solve this equation, we can first multiply both sides by 2 to eliminate the fraction: 2(3x - 2) = x + 16.
- Simplifying this gives us 6x - 4 = x + 16.
- Next, we can isolate the variable by subtracting x from both sides: 6x - x - 4 = 16.
- This simplifies to 5x - 4 = 16.
- Finally, we can isolate x by adding 4 to both sides: 5x - 4 + 4 = 16 + 4.
- This gives us 5x = 20.
- Dividing both sides by 5 results in x = 4.
- Therefore, the dogwood tree is 4 years old.
Substituting this value back into the equation for the ginkgo tree's age, we have 3(4) - 2 = 12 - 2 = 10. So, the ginkgo tree is 10 years old.
Complete question:
A park has a ginkgo tree, a dogwood tree, and 2 blue spruce trees. The blue spruce trees are 8 years old. The ginkgo tree is 2 years less than three times the age of the dogwood tree. The ginkgo tree is also half the sum of the ages of the dogwood tree and both of the blue spruce trees. Write and solve an equation to find the ages of the ginkgo and dogwood trees.
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Rewritten by : Jeany