370 College freshmen were interviewed. 200 were registered for an Advanced Math class. 270 were registered for an English class 220 were registered for a Sport Activity class. 100 were registered for both Math and English. 50 were registered for both Sport and English but not Math. 70 were registered for Math, Sport, and English.

a) How many signed up only for a Math class?
b) How many signed up for neither Math nor English?
c) How many signed up for an English class and at least one other class?
d) The cost for only one class per month is $100, for two - $150 and for three -$200. What is the total fee for all the students enrolled in classes?

Step-by-step explanation:

To aid in understanding, draw three circles...

100 were registered for both Math and English.

50 were registered for both Sport and English but not Math.

70 were registered for Math, Sport, and English.

From here we will be able to calculate for those that signed up for only English class: Total number of students that signed up for english class

a. none signed up only for Maths (refer to attached document)

b. How many signed up for neither Math nor English meaning they signed up for only sports which is 70 from the venn diagram in the attachment.

c. How many signed up for an English class and at least one other class?

From the venn diagram:

we could have an English class and maths class - 100

we could also have an a English class and sports - 50

Thus total is 150.

d. What is the total fee for all the students enrolled in classes

From the diagram, 120 (english only and sport only) enrolled for only one class = 120 x $100 = $12,000

From the diagram, 180 (english and sport, maths and sport and english and maths) enrolled for two classes = 180 x $150 = $27,000

From the diagram, only 70 enrolled for the three classes = 70 x $200 = $14,000

Total fees = $12,000 + $27,000 + $14,000 = $53,000

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap