Final answer:
There are 7 people who like only green beans. To serve 8 people who will eat corn, 4 cups of corn are needed for dinner.
Step-by-step explanation:
To determine how many people like only green beans, we use the information provided: there are 15 people coming to dinner, 5 of whom like both vegetables, and 3 people like only corn. First, we subtract the number of people who like both vegetables from the total number of guests:
15 total guests - 5 who like both = 10 guests left
Next, we subtract the number of people who like only corn from the remaining number of guests to find out how many people like only green beans:
10 guests left - 3 who like only corn = 7 people who like only green beans.
For the second part of the question, if a serving size for veggies is half a cup and 3 people like only corn, plus 5 people like both (and assuming they will also eat corn), we calculate the total amount of corn required:
3 people (only corn) + 5 people (both) = 8 people eating corn
Since each person eats half a cup, we simply multiply the number of people eating corn by the serving size:
8 people × 0.5 cups/person = 4 cups of corn needed for dinner.