Final answer:
7 guests times half a cup per guest equals 3.5 cups of corn needed for the dinner.
Step-by-step explanation:
To determine how many people like only green beans, we need to take into account the number of guests and the preference for veggies. If 2/5 of the guests like both veggies, this implies that 2/5 of the ten guests like both corn and green beans, which is 4 guests. We are told 3 people like only corn, so by subtracting this number from the total number of ten guests, we can infer that 3 guests like only green beans (10 - 4 - 3 = 3).
Next, to calculate how many cups of corn are needed for dinner, we need to consider the serving size. Since a serving size for veggies is half a cup and four guests like both vegetables, and three guests like only corn, we have a total of 7 guests who like corn (4 + 3 = 7). Thus, 7 guests times half a cup per guest equals 3.5 cups of corn needed for the dinner.