Final answer:
After calculating the number of students liking each food item—hamburgers (7), hot dogs (15), and pizza (2)—we concluded that 24 students like one of these foods, leaving 11 students who do not like any of the mentioned foods.
Step-by-step explanation:
The question asks us to calculate the number of students who do not like hamburgers, hot dogs, or pizza from a group of 35 students. To find this, we need to determine how many students like each of these foods and then subtract that total from the original number of students.
First, let's calculate the number of students who like hamburgers. Since 1/5 of the students like hamburgers, we multiply 35 by 1/5 to get 7 students.
Next, we calculate the number of students who like hot dogs. 3/7 of the students like hot dogs, so we multiply 35 by 3/7 to get 15 students.
Finally, for pizza, it's a bit tricky because the fraction given is 7 2/35, which is not a valid fraction of the total since it exceeds the number of students. Assuming that there's a typographical error and the correct fraction should be 2/35, we multiply 35 by 2/35 to get 2 students who like pizza.
Now, we add the number of students who like hamburgers, hot dogs, and pizza together: 7 + 15 + 2 = 24 students. We subtract this from the total number of students (35) to find how many students are left that don't like hamburgers, hot dogs, or pizza: 35 - 24 = 11 students.