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.

Question

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.

Answer 1

Plant A: y = 3x + 8

Plant B: y = 2x + 12

Answer 2

when will the plants be exactly the same height

Answer 3

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.