A gardener is planting two types of trees: Type A is 10 feet tall and grows at a rate of 10 inches per year. Type B is 6 feet tall and grows at a rate of 16
Mathematics
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Question
A gardener is planting two types of trees: Type A is 10 feet tall and grows at a rate of 10 inches per year. Type B is 6 feet tall and grows at a rate of 16 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
1 Answer

1. User Answers FRESHPRNCE
Answer:
8
Stepbystep explanation:
Firstly, we want to convert all values to inches, (1 ft = 12 inches)
So,
Type A is 120 inches tall and Type B is 72 inches tall.
Now,
Type A grows at 10 inches per year and Type B grows at 16 inches per year.
Let x be the number of years passed,
so the height of Type A plants will be [tex]120 + 10x[/tex] after x years have passed.
Similarly, Type B plants will be [tex]72 + 16x[/tex] after x years.
Now, we can equate the two equations to find x.
[tex]120 +10x=72 +16x[/tex]
[tex]6x = 48[/tex]
[tex]x=8[/tex]
Therefore, the number of years it will take for these trees to be the same height is 8.