Question

Hans is planting a garden with snapdragons and daisies. The table shows some possible combinations of the two plants. If Hans plants 29 daisies, how many snapdragons will he plant?

Number of

Snapdragons, x

Number of

Daisies, y

11 34
12 33
13 32
14 31


(2 points)
The equation that models the scenario is
.

Hans will plant
Snapdragons.

Answer 1

To find the equation that models the relationship between the number of snapdragons (x) and the number of daisies (y), we can observe the data points provided.

From the data:
- When there are 11 snapdragons, there are 34 daisies.
- When there are 12 snapdragons, there are 33 daisies.
- When there are 13 snapdragons, there are 32 daisies.
- When there are 14 snapdragons, there are 31 daisies.

From this, we can see that for each increase of 1 snapdragon, the number of daisies decreases by 1. This suggests a linear relationship.

Thus, we can express this in an equation format, where:
- Number of daisies, \( y \)
- Number of snapdragons, \( x \)

The change in daisies can be characterized by:

\[
y = 45 - x
\]

To find the constant (in this case, 45), we can use any pair. For example, using \( x = 11 \) and \( y = 34 \):

\[
34 = 45 - 11 \\
34 = 34 \quad \text{(true)}
\]

This relationship holds for all the points provided.

Now, to find out how many snapdragons Hans will plant when he plants 29 daisies (\( y = 29 \)), we can substitute 29 into our equation:

\[
29 = 45 - x
\]

Rearranging this to solve for \( x \):

\[
x = 45 - 29 \\
x = 16
\]

So Hans will plant **16 snapdragons**.

### Summary
The equation that models the scenario is:
\[
y = 45 - x
\]
Hans will plant **16 snapdragons**.