I assume that you meant 9 study French only. Otherwise, it's impossible to have 9 who study French and also 9 who study French and History, and x>0 who study all three.
That said, the Venn diagram makes it clear that
9+7+8+9+1+9+x = 38
x = 2
and now you know everything necessary.
n a class of 38 students, each student
studies at least one of the following subjects:
French, Mathematics and History. The following
table gives further details of the subject studied.
French 9
Mathematics only 8
History only 1
French & Math. 7
French & History 9
History & Math. 8
a) If x is the number of students who
studies all three subjects, illustrate the
information on a Venn diagram.
b) Write an equation in x involving the
number of students in the region of the
diagram.
c) Find the number of students who stdy
i) All the 3 subjects
ii) French
2 answers
a) Here's the Venn diagram:
_______________
/ / / /
/ F / M / H /
/_____/_____/____/
| / | \
| / | \
| / | \
/ F & M / F & H / H & M/
/________/________/_______/
b) The equation in x can be written as:
9 + 7 + 8 + 9 + 1 + 9 + x = 38
c)
i) All three subjects: x = 2
ii) French: 9 + 7 + 9 + 2 = 27
_______________
/ / / /
/ F / M / H /
/_____/_____/____/
| / | \
| / | \
| / | \
/ F & M / F & H / H & M/
/________/________/_______/
b) The equation in x can be written as:
9 + 7 + 8 + 9 + 1 + 9 + x = 38
c)
i) All three subjects: x = 2
ii) French: 9 + 7 + 9 + 2 = 27
6 answers