Algebraically determine exactly how many years it will take for these trees to be the same height.

Question

A gardener is planting two types of trees: Type A is 3 feet tall and grows at a rate of 23 inches per year. Type B is 8 feet tall and grows at a rate of 17 inches per year Algebraically determine exactly how many years it will take for these trees to be the same height.

Answer 1

1 feet = 12 inches 

3 feets= 36 inches

8 feets = 96 inches

 

Assume the year that it would take to these trees have the same height is : x (years)

 

After x years, type A tree has heigth: 36 +23x (inches)

 

After x years, type B tree has heigth: 96 +17x (inches)

 

We have  36+23x = 96+17x

Solve the equation, we have x=10

 

Conclusion: It will take 10 years to these trees have the same height.