A gardener is planting two types of trees:

Type A is 3 feet tall and grows at a rate of 15 inches per year.

Type B is 6 feet tall and grows at a rate of 11 inches per year.

Algebraically determine exactly how many years it will take for these trees to be the same height.
i dont get it ive tried everything that i know and still got stuck

Solution:

Let "x" be the number of years

Type A is 3 feet tall and grows at a rate of 15 inches per year

1 feet = 12 inches

3 feet = 12 x 3 = 36 inches

Equation: 36 + 15x eqn 1

Type B is 6 feet tall and grows at a rate of 11 inches per year

6 feet = 6 x 12 = 72 inches

Equation: 72 + 11x eqn 2

For both trees to be of same height, eqn 1 must be equal to eqn 2

36 + 15x = 72 + 11x

15x - 11x = 72 - 36

4x = 36

Thus it takes 9 years for both trees to be of same height

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

need points to ask question

step-by-step explanation: