\begin{tabular}{|c|c|}
\hline
\begin{tabular}{c}
Number of \\
snapdragons, [tex]$x$[/tex]
\end{tabular} & \begin{tabular}{c}
Number of \\
daisies, [tex]$y$[/tex]
\end{tabular} \\
\hline
11 & 34 \\
\hline
12 & 33 \\
\hline
13 & 32 \\
\hline
14 & 31 \\
\hline
\end{tabular}

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?

The equation modeling the scenario is:

[tex]\[ x + y = 45 \][/tex]

Substitute [tex]\( y = 29 \)[/tex]:

[tex]\[ x + 29 = 45 \][/tex]

Solve for [tex]\( x \)[/tex]:

[tex]\[ x = 45 - 29 \][/tex]

[tex]\[ x = 16 \][/tex]

Hans will plant 16 snapdragons.



Answer :

Let's carefully analyze the problem step-by-step to determine how many snapdragons Hans will plant if he plants 29 daisies.

### Step-by-Step Solution:

1. Understanding the Given Data:
The provided table shows different combinations of snapdragons ([tex]\(x\)[/tex]) and daisies ([tex]\(y\)[/tex]) that Hans could plant:

[tex]\[ \begin{tabular}{|c|c|} \hline \text{Number of snapdragons, } x & \text{Number of daisies, } y \\ \hline 11 & 34 \\ \hline 12 & 33 \\ \hline 13 & 32 \\ \hline 14 & 31 \\ \hline \end{tabular} \][/tex]

2. Identifying the Relationship:
By examining the data, we can see a pattern in the numbers:
- When [tex]\( x = 11 \)[/tex], [tex]\( y = 34 \)[/tex]
- When [tex]\( x = 12 \)[/tex], [tex]\( y = 33 \)[/tex]
- When [tex]\( x = 13 \)[/tex], [tex]\( y = 32 \)[/tex]
- When [tex]\( x = 14 \)[/tex], [tex]\( y = 31 \)[/tex]

For each pair, the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex] can be observed:

[tex]\[ x + y = 45 \][/tex]

3. Formulating the Equation:
Based on the observed relationship, the equation linking [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is:

[tex]\[ x + y = 45 \][/tex]

4. Solving the Equation:
We need to determine [tex]\( x \)[/tex] when [tex]\( y = 29 \)[/tex]:

[tex]\[ x + 29 = 45 \][/tex]

5. Solving for [tex]\( x \)[/tex]:
[tex]\[ x = 45 - 29 = 16 \][/tex]

6. Conclusion:
If Hans plants 29 daisies, he will plant 16 snapdragons.

### Final Answer:
Hans will plant 16 snapdragons.