A gardener is planting two types of trees: Type A is 5 feet tall and grows at a rate of 19 inches per year. Type B is 7 feet tal

Question

4 years ago

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A gardener is planting two types of trees: Type A is 5 feet tall and grows at a rate of 19 inches per year. Type B is 7 feet tal

l 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.

Mathematics

1 answer:

iren [92.7K] · Answer 1 · 2022-02-10T13:13:29+03:00

it will take 8 months for these trees to be same height

Further explanation:

Let x be the number of years then,

Type A is 5 feet tall and grows at a rate of 19 inches per year

The expression for Type A is:

5+19x

Type B is 7 feet tall and grows at a rate of 16 inches per year

The expression for Type B is:

7+16x

Putting both of them equal will give us the time in which both to be same height

$5+19x=7+16x\\Subtracting 16x from both sides\\5+19x-16x=7+16x-16x\\5+3x=7\\Subtracting 5 from both sides\\5+3x-5=7-5\\3x=2\\x=\frac{2}{3}\\Mutiplying\ numerator\ and\ denominator\ of\ fraction\ by\ 4\\x=\frac{8}{12}$

Hence, it will take 8 months for these trees to be same height

Keywords: Rate of Change, Linear Equations

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