Questions: The relationship between the time in minutes and pieces of bamboo eaten is proportional. Ling ling, the panda, can eat 6 pieces of bamboo in 4 minutes. Find the constant of proportionality.

Solution Steps

The relationship between time $x$ (in minutes) and pieces of bamboo $y$ is proportional. This means: $$y = kx$$ where $k$ is the constant of proportionality.

Given that Ling Ling eats 6 pieces of bamboo in 4 minutes, we can substitute $x = 4$ and $y = 6$ into the equation: $$6 = k \cdot 4$$ Solving for $k$: $$k = \frac{6}{4} = 1.5$$ The constant of proportionality is $k = 1.5$.

Using the equation $y = 1.5x$, we can calculate the missing values in the table:

1. For $x = 0$: $$y = 1.5 \cdot 0 = 0$$
2. For $x = 1$: $$y = 1.5 \cdot 1 = 1.5$$
3. For $x = 2$: $$y = 1.5 \cdot 2 = 3$$
4. For $x = 3$: $$y = 1.5 \cdot 3 = 4.5$$
5. For $x = 4$: $$y = 1.5 \cdot 4 = 6$$

The completed table is:

\begin{tabular}{|c|c|} \hline Time in Minutes, \( x \) & Pieces of Bamboo, \( y \) \\ \hline 0 & 0 \\ \hline 1 & 1.5 \\ \hline 2 & 3 \\ \hline 3 & 4.5 \\ \hline 4 & 6 \\ \hline \end{tabular}

Final Answer