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. what are the correct values of a, b, c, d, and e? 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

Explanation:

Step1: Find the value of \(e\)

Total number of students is \(75\), number of students who like geometry is \(53\). Using the formula \(e=75 - 53\).

$$e = 22$$

Step2: Find the value of \(d\)

Total number of students is \(75\), number of students who like algebra is \(45\). Using the formula \(d=75 - 45\).

$$d = 30$$

Step3: Find the value of \(c\)

Number of students who like geometry is \(53\), \(a + c=53\). Also, \(d = 30\) (from step 2), and \(c + 6=d\). So \(c=d - 6\). Substitute \(d = 30\) into the equation.

$$c=30 - 6=24$$

Step4: Find the value of \(a\)

Since \(a + c=53\) and \(c = 24\), then \(a=53 - c\).

$$a=53 - 24 = 29$$

Step5: Find the value of \(b\)

Since \(a + b=45\) and \(a = 29\), then \(b=45 - a\).

$$b=45 - 29=16$$

Answer:

\(a = 29, b = 16, c = 24, d = 30, e = 22\) (the fourth option)