Kristin bought two sunflower plants. Plant A is 8 inches tall and is growing at a rate of 3 inches per week. Plant B is 12 inches tall and is growing at a rate of 2 inches per week. Write the two equations to represent each sunflower plant if the plants to continue to grow at the same rate. In your equations, x%0D%0A%0D%0A represents the number of weeks, and y%0D%0A%0D%0A represents the height of the plant in inches.
Plant A: y = 3x + 8
Plant B: y = 2x + 12
when will the plants be exactly the same height
To find out when the plants will be exactly the same height, we set the two equations equal to each other:
3x + 8 = 2x + 12
Now, we solve for x:
3x - 2x = 12 - 8
x = 4
Therefore, the plants will be exactly the same height after 4 weeks.
We can confirm this by substituting x=4 back into one of the equations:
For Plant A:
y = 3(4) + 8
y = 12 + 8
y = 20
For Plant B:
y = 2(4) + 12
y = 8 + 12
y = 20
Both plants will be 20 inches tall after 4 weeks.