To determine how many heads of lettuce Timothy would need to feed 275 guests, we can set up a proportion based on the number of heads of lettuce required for 100 guests.
We know that:
- 37 heads of lettuce are needed for 100 guests.
We want to find the number of heads of lettuce (x) needed for 275 guests.
Setting up the ratio, we have:
\[ \frac{37 \text{ heads of lettuce}}{100 \text{ guests}} = \frac{x \text{ heads of lettuce}}{275 \text{ guests}} \]
Now, we can solve for x by cross-multiplying:
\[ 37 \cdot 275 = 100 \cdot x \]
Calculating \(37 \cdot 275\):
\[ 37 \cdot 275 = 10275 \]
Now, we can express that as:
\[ 100x = 10275 \implies x = \frac{10275}{100} = 102.75 \]
Since we can't have a fraction of a head of lettuce in practical terms, Timothy would need approximately 103 heads of lettuce to feed 275 guests.
Thus, the appropriate ratio illustrating how many heads of lettuce Timothy would need for 275 guests is:
\[ \frac{37}{100} = \frac{103}{275} \]
If you provide the options (A, B, C, D), I can help identify the correct one based on this calculation.