Answer:
[tex]A=3.5w+5[/tex] and [tex]B=1.5w+6[/tex] .
Step-by-step explanation:
Let w represent number of weeks.
We have been given that plant A is 5 inches when planted and grows an average of 3.5 inches per week.
The height of plant A in w weeks would be [tex]3.5w[/tex]. The total height of plant A is w weeks would be initial height plus height in w weeks.
[tex]A=3.5w+5[/tex]
We are also told that plant B is 6 inches when planted and grows an average of 1.5 inches per week.
The height of plant B in w weeks would be [tex]1.5w[/tex]. The total height of plant B is w weeks would be initial height plus height in w weeks.
[tex]B=1.5w+6[/tex]
To find the number of weeks it takes for both plants to be the same height, we need to equate both equation as:
[tex]3.5w+5=1.5w+6[/tex]
Combine like terms:
[tex]3.5w-1.5w=6-5[/tex]
[tex]2w=1[/tex]
[tex]\frac{2w}{2}=\frac{1}{2}[/tex]
[tex]w=0.5[/tex]
Therefore, after 0.5 week the height of both trees will be equal and our required system would be [tex]A=3.5w+5[/tex] and [tex]B=1.5w+6[/tex] .
