Jeremy made a Venn diagram showing the number of students in his class who own types of pets. There are 32 students in his class
. In addition to the information in the Venn diagram, Jeremy knows half of the students have a dog, $\frac{3}{8}$ have a cat, six have some other pet and five have no pet at all. How many students have all three types of pets (i.e. they have a cat and a dog as well as some other pet)?
1 answer:
The Venn diagram
is attached in the figure.
Total number of students = 32
Number of students have a dog = 0.5 *32 = 16
Number of students have a cat = (3/8) * 32 = 12
Number of students have other pets = 6
Number of students have no pets = 5
From the Venn diagram:
Number of students have a dog = x+y+z+10
Number of students have a cat = x+z+w+9
Number of students have other pets = y+z+w+2
Total number of students have no pets = 32 – (x+y+z+w+21)
So, as a conclusion for the above information
x+y+z+10 = 16 (1)
x+z+w+9 = 12 (2)
y+z+w+2 = 6 (3)
32 – (x+y+z+w+21) = 5 (4)
By solving the system of equations to find x , y , z , w
x = 2 , y = 3 , z = 1 , w = 0
By using Venn diagram
Number of students <span>have all three types of pets</span> = z = 1 student
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