In a class, every student knows French or German (or both). 15 students know French, and 17 students know German
What is the smallest possible number of students in that class?
17
If all 15 of the people that speak French know German then the lowest amount of people that are in the class would be 17.
To find the smallest possible number of students in the class, we need to determine the number of students who know both French and German.
Let's assume that x students know both French and German.
We are given that 15 students know French and 17 students know German. Since x students know both French and German, we can subtract x from both of these numbers to find the number of students who know only one language.
So, the number of students who know only French is 15 - x, and the number of students who know only German is 17 - x.
To find the total number of students in the class, we can add up the number of students who know only French (15 - x), the number of students who know only German (17 - x), and the number of students who know both French and German (x).
Total number of students in the class = (15 - x) + (17 - x) + x
Simplifying the expression, we get:
Total number of students in the class = 15 + 17 - x - x + x
Total number of students in the class = 32 - x
Since we want to find the smallest possible number of students, we want to minimize the value of x.
Therefore, the smallest possible number of students in the class is 32.
To find the smallest possible number of students in the class, we can calculate the total number of students by adding the number of students who know French and the number of students who know German, and then subtracting the number of students who know both French and German.
Let's use the given information:
Number of students who know French = 15
Number of students who know German = 17
Since the question states that every student knows French or German (or both), we can assume that there is at least one student who knows both languages. To find the smallest possible number of students, let's assume that there is only one student who knows both French and German.
Number of students who know both French and German = 1
Now, we can calculate the smallest possible number of students in the class:
Total number of students = French + German - Both
= 15 + 17 - 1
= 31
Therefore, the smallest possible number of students in that class is 31.