By using Venn diagram method, the smallest and the largest number of students that intend to study both French and German are 21 and 49 students respectively.
Given that Larousse Language College will have 201 students in the Sixth Form next year. And between 70% and 75% of the students intend to study French. Also, between 40% and 50% of the students intend to study German.
If all students study either French or German or both, the least number of students that will study French will be
70/100 x 201
140. 7
Which means 141 students
The least number of students that will study German will be
40/100 x 201
80.4
That means 81 students
Also, the maximum number of students that will study French will be
75/100 x 201
150.75
That is 150 students ( Because approximation can't be done twice)
And the maximum number of students that will study German will be
50/100 x 201
100 students ( Because approximation can't be done twice)
a.) The smallest number of students that intend to study both French and German can be calculated as followed
Let the smallest number be x
141 - x + x + 81 - x = 201
222 - x = 201
- x = 201 - 222
-x = - 21
x = 21
b.) The largest number of students that intend to study both French and German can be calculated as followed
Let the largest number be y
150 - y + y + 100 - y = 201
250 - y = 201
- y = 201 - 250
-y = - 49
y = 49
Therefore, The smallest and the largest number of students that intend to study both French and German are 21 and 49 students respectively.
Learn more about Venn diagram here: https://brainly.com/question/9384416
