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 point) Plant A: y= Plant B: y= Question 2 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 . Skip to navigation

Answer 1

To represent the growth of the two plants, we can set up the following equations:

**For Plant A:**
- Initial height = 8 inches
- Growth rate = 3 inches per week

The equation for Plant A, where \(x\) is the number of weeks and \(y\) is the height in inches, is:
\[
y = 8 + 3x
\]

**For Plant B:**
- Initial height = 12 inches
- Growth rate = 2 inches per week

The equation for Plant B is:
\[
y = 12 + 2x
\]

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**Question 2: When will the plants be exactly the same height?**

To find out when the plants will be the same height, we need to set the two equations equal to each other:

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

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

1. Subtract \(2x\) from both sides:
\[
8 + 3x - 2x = 12
\]
Simplifying this gives:
\[
8 + x = 12
\]

2. Subtract 8 from both sides:
\[
x = 12 - 8
\]
\[
x = 4
\]

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

Thus, the answers to the questions are:
- Plant A: \(y = 8 + 3x\)
- Plant B: \(y = 12 + 2x\)
- The plants will be exactly the same height during week **4**.