Question

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. algebra vs. geometry

	likes geometry	does not like geometry	total
does not like algebra	c	6	d
total	53	e	75

what are the correct values of a, b, c, d, and e?
o a = 16, b = 29, c = 22, d = 30, e = 24
o a = 29, b = 16, c = 30, d = 22, e = 24
o a = 16, b = 29, c = 24, d = 22, e = 30
o a = 29, b = 16, c = 24, d = 30, e = 22

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 algebra and geometry

We know that $n(A\cup G)=n(A)+n(G)-n(A\cap G)$, where $n(A)$ is the number of students who like algebra, $n(G)$ is the number of students who like geometry and $n(A\cup G)$ is the number of students who like at least one of them. Given $n(A) = 45$, $n(G)=53$ and $n(A\cup G)=69$. Then $69 = 45+53 - n(A\cap G)$, so $n(A\cap G)=45 + 53-69=29$, so $a = 29$.

Step3: Find the value of $b$

Since $n(A)=45$ and $a = 29$, then $b=45 - 29 = 16$.

Step4: Find the value of $c$

Since $n(G)=53$ and $a = 29$, then $c=53 - 29 = 24$.

Step5: Find the value of $d$

The number of students who do not like algebra is $d=75 - 45=30$.

Step6: Find the value of $e$

The number of students who do not like geometry is $e=75 - 53 = 22$.

Answer:

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