Question

Plant A is 5 inches when planted and grows an average of 3.5 inches per week. Plant B is 6 inches when planted and grows an average of 1.5 inches per week. Which system of equations can be used to determine the number of weeks it takes for both plants to be the same height?

Answer 1

`A=3.5w+5` and
`B=1.5w+6` .

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
`3.5w`. The total height of plant A is w weeks would be initial height plus height in w weeks.

`A=3.5w+5`

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
`1.5w`. The total height of plant B is w weeks would be initial height plus height in w weeks.

`B=1.5w+6`

To find the number of weeks it takes for both plants to be the same height, we need to equate both equation as:

`3.5w+5=1.5w+6`

Combine like terms:

`3.5w-1.5w=6-5`

`2w=1`

`(2w)/(2)=(1)/(2)`

`w=0.5`

Therefore, after 0.5 week the height of both trees will be equal and our required system would be
`A=3.5w+5` and
`B=1.5w+6` .