A gardener is planting two types of trees: Type A is 5 feet tall and grows at a rate of 13 inches per year. Type B is 3 feet tall and grows at a rate of 21 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

Question

Mathematics

Devon Hill

12 August, 22:54

A gardener is planting two types of trees: Type A is 5 feet tall and grows at a rate of 13 inches per year. Type B is 3 feet tall and grows at a rate of 21 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

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Answers (1)

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Melvin Case · Answer 1

Answer:it will take 0.25 years

Step-by-step explanation:

Let x represent the number of years that it will take for type A and tree B to be the same height.

Let y represent the height of type A after x years.

Let z represent the height of type B after x years.

Type A is 5 feet tall and grows at a rate of 13 inches per year. This means that

y = 5 + 13x

Type B is 3 feet tall and grows at a rate of 21 inches per year. This means that

z = 3 + 21x

To determine the number of years it will take both trees to be of the same height, we would equate equation y to z. It becomes

5 + 13x = 3 + 21x

21x - 13x = 5 - 3

8x = 2

x = 2/8 = 0.25 years