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A weeping willow that is 15 feet in height grows to a maximum height of 35 feet in
y years at a constant rate of 24 inches per year. Which of the following equations best describes this situation?
1 foot
=12 inches
Choose 1 answer:
(A)
35=15+2y
(B)
35=15+24 y
(c)
35=15-2y
(D)
35=15-24 y

A weeping willow that is $15$ feet in height grows to a maximum height of $35$ feet in $y$ years at a constant rate of $24$ inches per year. Which of the following equations best describes this situation? $\newline$ $1$ foot $=12$ inches $\newline$ Choose $1$ answer: $\newline$ (A) $35=15+2 y$ $\newline$ (B) $35=15+24 y$ $\newline$ (C) $35=15-2 y$ $\newline$ (D) $35=15-24 y$

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Write a linear inequality: word problems

Full solution

Q. A weeping willow that is

15

feet in height grows to a maximum height of

35

feet in

y

years at a constant rate of

24

inches per year. Which of the following equations best describes this situation?

\newline

1

foot

=12

inches

\newline

Choose

1

answer:

\newline

(A)

35=15+2 y

\newline

(B)

35=15+24 y

\newline

(C)

35=15-2 y

\newline

(D)

35=15-24 y

Convert growth rate to feet: We need to convert the growth rate from inches to feet because the height of the tree is given in feet. Since there are $12$ inches in a foot, we divide the growth rate by $12$ to convert it to feet per year. $\newline$ Calculation: $\frac{24 \text{ inches per year}}{12 \text{ inches per foot}} = 2 \text{ feet per year}$
Set up the growth equation: Now we can set up an equation to represent the growth of the tree. The tree starts at $15$ feet and grows at a rate of $2$ feet per year for $y$ years. The maximum height the tree will reach is $35$ feet. $\newline$ Equation: Initial height + (Growth rate $\times$ Number of years) = Maximum height $\newline$ Substitute the known values: $15$ feet + ( $2$ feet/year $\times$ $y$ years) = $35$ feet
Simplify the equation: Simplify the equation to find the one that matches the choices given. $\newline$ $15 + 2y = 35$ $\newline$ This equation represents the growth of the tree in feet over $y$ years.

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