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.
