Question

Counting Cats and DogsPOW ID 45-13ProblemPrintLin's math class surveyed all 360 students in their school about their petsHere's what they found:• 193 of the students have dogs• 160 of the students have cats• 83 of the students have neither a dog nor a catHow many students have both a dog and a cat?ExtraExtra: What percent of the students have a cat but not a dog? ExplainPhoto: Kaytee Riek

Answer 1

Let D represent number of students that have dog

Let C represent number of students that have cat

n(U) = 360

n(D) = 193

n(C)= 160

`n\mleft(DuC\mright)^I=\text{ 83}`

Let n (D n C) be y

From the Venn diagram,

83 + 193-y + y+160-y = 360

436-y=360

-y = 360-436

-y = -76

y=76

Therefore, 76 students have both dogs and cat

Part two

Number of the students that have a cat but not a dog = 160-y

=160-76

=84

% of the students have a cat but not a dog = 84/360 x 100

=23.33%