To determine the number of heads of lettuce Timothy needs for 275 guests, we can set up a ratio based on the information given.
We know that:
37 heads of lettuce are needed for 100 guests.
We want to find out how many heads of lettuce (x) are needed for 275 guests.
We can use the ratio:
\[ \frac{37 \text{ heads}}{100 \text{ guests}} = \frac{x \text{ heads}}{275 \text{ guests}} \]
Cross-multiplying to solve for x:
\[ 37 \times 275 = 100 \times x \]
Now calculate \(37 \times 275\):
\[ 37 \times 275 = 10275 \]
So we have:
\[ 10275 = 100x \]
Now, divide both sides by 100 to solve for x:
\[ x = \frac{10275}{100} = 102.75 \]
Since Timothy can't use a fraction of a head of lettuce, he would need to round up, meaning he would need 103 heads of lettuce to feed 275 guests.
Thus, the ratio illustrating how many heads of lettuce he would need to feed 275 guests is:
\[ \frac{37}{100} = \frac{103}{275} \]
This is the correct ratio that illustrates the relationship of heads of lettuce needed to the number of guests.