The number of students who are enrolled in math and biology, but not English are:
100 students
Step-by-step explanation:
Let x be the number of students enrolled in Math and Biology but not English.
Hence, with the help of the Venn diagram attached to the answer we may conclude that the sum of all the students that are represented is equal to the number of students attending the school.
i.e. we have:
Hence, the number of students who get enrolled in Math and Biology but not English are:
Using the symbols in the Venn diagram, we want to find A given that
B = 16
C = 15
D = 30
and given that 25 students don't take any of these courses.
There are 200 students total, so we need to have A plus the total number of students given in the diagram sum to 200. This means
(math only) + (English only) + (biology only) + (math and English, no biology) + (math and biology, no English) + (English and biology, no math) + (all three) + (none of the three) = 200
The number of students who are enrolled in math and biology, but not English are:
100 students
Step-by-step explanation:
Let x be the number of students enrolled in Math and Biology but not English.
Hence, with the help of the Venn diagram attached to the answer we may conclude that the sum of all the students that are represented is equal to the number of students attending the school.
i.e. we have:
Hence, the number of students who get enrolled in Math and Biology but not English are:
a) The sum of the enrollments in chemistry (60), physics (45), and biology (30) counts those triply enrolled 3 times and those doubly-enrolled twice. This sum will exceed the total number of students by 1 times those double-enrolled and twice those triply-enrolled.
We know that there are 10 students triply-enrolled, so the difference ...
(60 +45 +30) -2(10) = 15
is the number of doubly-enrolled students.
There are 15 students enrolled in exactly 2 science classes.
__
b) There are 9+4 = 13 students doubly-enrolled in physics and something else. Using the result from part A, there will be 15 -13 = 2 students doubly-enrolled in chemistry and biology, but not physics.
a) The sum of the enrollments in chemistry (60), physics (45), and biology (30) counts those triply enrolled 3 times and those doubly-enrolled twice. This sum will exceed the total number of students by 1 times those double-enrolled and twice those triply-enrolled.
We know that there are 10 students triply-enrolled, so the difference ...
(60 +45 +30) -2(10) = 15
is the number of doubly-enrolled students.
There are 15 students enrolled in exactly 2 science classes.
__
b) There are 9+4 = 13 students doubly-enrolled in physics and something else. Using the result from part A, there will be 15 -13 = 2 students doubly-enrolled in chemistry and biology, but not physics.