Hans is planting a garden with snapdragons and daisies. The table shows some possible combinations of the two plants.

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

If Hans plants 29 daisies, how many snapdragons will he plant?
The equation $\square$ models the scenario.
Hans will plant $\square$ snapdragons.

Observe that the number of snapdragons and daisies always sums to 45, so the equation is x + y = 45 .
Substitute the number of daisies, y = 29 , into the equation: x + 29 = 45 .
Solve for x by subtracting 29 from both sides: x = 45 − 29 = 16 .
Hans will plant 16 ​ snapdragons.

Explanation

Problem Analysis Let's analyze the problem. We are given a table that shows the relationship between the number of snapdragons ( x ) and the number of daisies ( y ) in Hans's garden. We need to find an equation that models this relationship and then use that equation to determine how many snapdragons Hans will plant if he plants 29 daisies.

Finding the Equation Looking at the table, we can see that as the number of snapdragons increases by 1, the number of daisies decreases by 1. This suggests a linear relationship between x and y . Let's test if the relationship is of the form x + y = c , where c is a constant. Using the first data point (11, 34), we have 11 + 34 = 45 . Let's check if this holds for the other points as well:



For (12, 33): 12 + 33 = 45
For (13, 32): 13 + 32 = 45
For (14, 31): 14 + 31 = 45

So, the equation that models the scenario is x + y = 45 .

Substituting the Value of y Now, we are given that Hans plants 29 daisies, which means y = 29 . We need to find the corresponding number of snapdragons, x . We can substitute y = 29 into the equation x + y = 45 :

x + 29 = 45

Solving for x To solve for x , we subtract 29 from both sides of the equation:

x = 45 − 29
x = 16

Final Answer Therefore, if Hans plants 29 daisies, he will plant 16 snapdragons.

Examples
Imagine you're arranging flowers in a vase. You know you want a total of 45 flowers, a mix of snapdragons and daisies. If you decide you want 29 daisies, this problem shows you how to calculate exactly how many snapdragons you'll need to complete the arrangement. This kind of problem helps in resource allocation, ensuring you have the right balance of different components to meet a specific total. It's useful in planning events, managing inventory, or even budgeting!

Answered by GinnyAnswer | 2025-07-08