Question

Students graphed the growth rate over several weeks of two plants in their classroom. The equations of both plants are given where x represents the time in weeks and y represents the heights of the plants in inches.

Plant A: y = 1.8x + 3.1
Plant B: y = 2.3x + 1.9
Approximately how many weeks will it take for both plants to reach the same height? Round your answer to the nearest tenth.
1.9 weeks
2.4 weeks
3.1 weeks
7.4 weeks

Answer 1

1.8x + 3.1 = 2.3x + 1.9
1.8x - 2.3x = 1.9 - 3.1
-0.5x = -1.2
x = -1.2 / -0.5
x = 2.4 weeks

Answer 2

B. 2.4 weeks

Explanation:

The equations for the growth rate of the plants are given by,

Plant A:
`y = 1.8x + 3.1`

Plant B:
`y =2.3x + 1.9`,

where y = height of the plants (in inches) and x = time (in weeks).

It is required to find the number of weeks after which the plants reach the same height.

As, the plants will reach the same height. So, we get,

`1.8x + 3.1=2.3x + 1.9`

i.e.
`0.5x=1.2`

i.e. x = 2.4

Hence, after 2.4 weeks, the height of both the plants will be the same.