Question

adrian has been planting young trees in his garden. the maple tree that is 20 inches tall is growing 4 inches per month, whereas the oak tree that is 50 inches tall is growing 1 inch each month. in a few months, the two trees will be the same height. what will that height be?
write a system of equations, graph them, and type the solution.

Explanation:

Step1: Define variables and equations

Let $m$ = number of months, $h$ = height (in inches).
Maple tree: $h = 20 + 4m$
Oak tree: $h = 50 + 1m$

Step2: Set equations equal (same height)

$20 + 4m = 50 + m$

Step3: Solve for $m$

Subtract $m$ and 20 from both sides:
$4m - m = 50 - 20$
$3m = 30$
$m = \frac{30}{3} = 10$

Step4: Find height at $m=10$

Substitute $m=10$ into maple tree equation:
$h = 20 + 4(10) = 20 + 40 = 60$

Answer:

The two trees will be the same height (60 inches) after 10 months.

Graph Notes (for plotting):

• For the maple tree: Plot points $(0, 20)$ and $(10, 60)$, draw a line through them.
• For the oak tree: Plot points $(0, 50)$ and $(10, 60)$, draw a line through them.
• The lines intersect at $(10, 60)$, which is the solution.