a group of 75 math students were asked whether they like algebra and whether they like geometry. a total of…

a group of 75 math students were asked whether they like algebra and whether they like geometry. a total of 45 students like algebra, 53 like geometry, and 6 do not like either subject. what are the correct values of a, b, c, d, and e? algebra vs. geometry likes geometry does not like geometry total likes algebra a b 45 does not like algebra c 6 d total 53 e 75 a = 16, b = 29, c = 22, d = 30, e = 24 a = 29, b = 16, c = 30, d = 22, e = 24 a = 16, b = 29, c = 24, d = 22, e = 30 a = 29, b = 16, c = 24, d = 30, e = 22

a group of 75 math students were asked whether they like algebra and whether they like geometry. a total of 45 students like algebra, 53 like geometry, and 6 do not like either subject. what are the correct values of a, b, c, d, and e? algebra vs. geometry likes geometry does not like geometry total likes algebra a b 45 does not like algebra c 6 d total 53 e 75 a = 16, b = 29, c = 22, d = 30, e = 24 a = 29, b = 16, c = 30, d = 22, e = 24 a = 16, b = 29, c = 24, d = 22, e = 30 a = 29, b = 16, c = 24, d = 30, e = 22

Answer

Explanation:

Step1: Find the number of students who like at least one subject

The total number of students is 75 and 6 do not like either subject. So the number of students who like at least one subject is $75 - 6=69$.

Step2: Find the number of students who like both subjects

Let the number of students who like both algebra and geometry be $a$. We know that the number of students who like algebra is 45 and the number who like geometry is 53. Using the formula $n(A\cup B)=n(A)+n(B)-n(A\cap B)$, where $n(A\cup B)$ is the number of students who like at least one subject, $n(A)$ is the number of students who like algebra, $n(B)$ is the number of students who like geometry and $n(A\cap B)$ is the number of students who like both. So $69 = 45+53 - a$, which gives $a=45 + 53-69=29$.

Step3: Find the value of $b$

Since the number of students who like algebra is 45 and $a = 29$, then $b=45 - 29 = 16$.

Step4: Find the value of $c$

Since the number of students who like geometry is 53 and $a = 29$, then $c=53 - 29 = 24$.

Step5: Find the value of $d$

The number of students who do not like algebra is $d$. We know that the number of students who do not like either subject is 6 and $c$ is the number of students who do not like algebra but like geometry. So $d=c + 6=24+6=30$.

Step6: Find the value of $e$

The total number of students who do not like geometry is $e$. We know that the total number of students is 75 and the number of students who like geometry is 53. So $e=75 - 53=22$.

Answer:

a = 29, b = 16, c = 24, d = 30, e = 22