Plant A: y = 3x + 8
Plant B: y = 2x + 12
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.
3 answers
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.
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.