Question

1. cameron and joseph both planted trees.

camerons tree was 1 foot tall when he planted it and it grows 2 feet every year.
josephs tree was 8 feet tall when he planted it and it grows $\frac{1}{4}$ of a foot every year.
(a) which system of equations could be used to represent the situation in context?
a $y = x + 1$
$y = x + 8$
b $y = 2x + 1$
$y = \frac{1}{4}x + 8$
c $y = x + 2$
$y = 8x + \frac{1}{4}$
d $y = \frac{1}{4}x + 1$
$y = 2x + 8$
(b) the solution is $(4, 9)$. what does the solution mean in context of the situation?
a after 9 years, both trees are 4 feet tall
b camerons tree is 4 feet tall and josephs tree is 9 feet tall
c after 4 years, both trees are 9 feet tall
d camerons tree is 4 years old and josephs tree is 9 years old

Explanation:

Part (a)

Step1: Define variables

Let $x$ = number of years since planting, $y$ = height of tree (ft).

Step2: Cameron's tree equation

Initial height = 1 ft, growth = 2 ft/year.
$y = 2x + 1$

Step3: Joseph's tree equation

Initial height = 8 ft, growth = $\frac{1}{4}$ ft/year.
$y = \frac{1}{4}x + 8$

The solution $(4,9)$ means $x=4$ (years since planting) and $y=9$ (height in feet). This corresponds to both trees being 9 feet tall 4 years after planting.

Answer:

B. $y=2x + 1$
D. $y=\frac{1}{4}x + 8$

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Part (b)