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)?
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three students have all three pets
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Answer:
Number of students have all three types of pets = z = 1 student
Step-by-step explanation:
The Venn diagram is attached in the figure below :
Total number of students = 32
Number of students have a dog = 0.5 × 32 = 16
⇒ x + y + z + 10 = 16
Number of students have a cat = (3/8) × 32 = 12
⇒ x + z + w + 9 = 12
Number of students have other pets = 6
⇒ y + z + w + 2 = 6
Number of students have no pets = 5
⇒ 32 - (x + y + z + w + 21) = 5
By solving these system of equations to find x , y , z , w
We get : x = 2 , y = 3 , z = 1 , w = 0
By using Venn diagram :
Number of students have all three types of pets = z = 1 student
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