To determine how many cups of sugar Quinn will need to make 14 pies, we can approach this problem using the method of linear interpolation. Linear interpolation helps us estimate values that are within the range of a set of known data points.
Given the data:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline \text{Number of Pies} & 3 & 5 & 9 \\
\hline \text{Cups of Sugar} & 1.5 & 2.5 & 4.5 \\
\hline
\end{array}
\][/tex]
We want to find out the number of cups of sugar needed for 14 pies.
Step-by-Step Solution:
1. Identify the Known Ratios:
- For 3 pies, it takes 1.5 cups of sugar.
- For 5 pies, it takes 2.5 cups of sugar.
- For 9 pies, it takes 4.5 cups of sugar.
2. Goal:
- Find the number of cups of sugar needed for 14 pies.
3. Estimate the Cups of Sugar:
- We need to estimate the number of cups of sugar based on the linear relationship between the number of pies and cups of sugar.
- Given that 14 pies is outside the known range of pies (between 3 and 9), we will logically extend the trend using the data provided.
4. Interpolation Calculation:
- When you look at the trend, the number of cups of sugar increases as the number of pies increases.
- By using the method of linear interpolation, it is determined that for 14 pies, the corresponding number of cups of sugar is approximately [tex]\( 4.5 \)[/tex] cups.
So, according to the interpolation of the given data points, Quinn will need 4.5 cups of sugar to make 14 pies.
Therefore, the correct answer is:
[tex]\[
\boxed{4.5}
\][/tex] cups
