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
represents the number of weeks, and y
represents the height of the plant in inches. (1 po

When will the plants be exactly the same height?

This question requires you to show your work.

(1 point)
The plants will be exactly the same height during week

Answer 1

Let's define the equations for each plant based on the information given.

For Plant A:
- Initial height: 8 inches
- Growth rate: 3 inches per week
- Equation:
\[
y_A = 8 + 3x
\]

For Plant B:
- Initial height: 12 inches
- Growth rate: 2 inches per week
- Equation:
\[
y_B = 12 + 2x
\]

Now we need to find out when the two plants will be exactly the same height. This means we will set the two equations equal to each other:

\[
8 + 3x = 12 + 2x
\]

Now, we can solve for \(x\):

1. Subtract \(2x\) from both sides:
\[
8 + x = 12
\]

2. Subtract 8 from both sides:
\[
x = 4
\]

Thus, the plants will be exactly the same height during week **4**.

To check:
- Height of Plant A after 4 weeks:
\[
y_A = 8 + 3(4) = 8 + 12 = 20 \text{ inches}
\]
- Height of Plant B after 4 weeks:
\[
y_B = 12 + 2(4) = 12 + 8 = 20 \text{ inches}
\]

Both plants will be 20 inches tall after 4 weeks, confirming that our solution is correct.