likes touring bikes does not like touring bikes total likes mountain bikes a b 47 does not like mountain…

likes touring bikes does not like touring bikes total likes mountain bikes a b 47 does not like mountain bikes c 5 d total 70 e 80 what are the correct values of a, b, c, d, and e? a = 42, b = 28, c = 33, d = 5, e = 10 a = 42, b = 5, c = 28, d = 33, e = 10 a = 5, b = 42, c = 28, d = 10, e = 33 a = 5, b = 10, c = 28, d = 33, e = 42

likes touring bikes does not like touring bikes total likes mountain bikes a b 47 does not like mountain bikes c 5 d total 70 e 80 what are the correct values of a, b, c, d, and e? a = 42, b = 28, c = 33, d = 5, e = 10 a = 42, b = 5, c = 28, d = 33, e = 10 a = 5, b = 42, c = 28, d = 10, e = 33 a = 5, b = 10, c = 28, d = 33, e = 42

Answer

Explanation:

Step1: Find the value of e

The total number of people surveyed is 80, and the number of people who like touring bikes is 70. So, the number of people who do not like touring bikes $e=80 - 70=10$.

Step2: Find the value of d

The number of people who do not like mountain - bikes and do not like touring bikes is 5, and the total number of people who do not like mountain bikes is d. Since the number of people who do not like touring bikes among those who do not like mountain bikes is 5 and $e = 10$, then $d=5 + c$. Also, from the total number of people surveyed (80) and the number of people who like mountain bikes (47), the number of people who do not like mountain bikes $d=80 - 47=33$.

Step3: Find the value of c

Since $d = 33$ and the number of people who do not like mountain bikes and do not like touring bikes is 5, then $c=d - 5=33 - 5=28$.

Step4: Find the value of b

The total number of people who like mountain bikes is 47, and the number of people who like mountain bikes and like touring bikes is a, and the number of people who like mountain bikes and do not like touring bikes is b. Also, $e = 10$ and the number of people who do not like touring bikes among those who like mountain bikes is b. Since the total number of people who do not like touring bikes is 10 and the number of people who do not like touring bikes and do not like mountain bikes is 5, then $b = 5$.

Step5: Find the value of a

The total number of people who like touring bikes is 70, and the number of people who do not like mountain bikes and like touring bikes is c. So, $a=70 - c$. Substituting $c = 28$, we get $a=70 - 28=42$.

Answer:

a = 42, b = 5, c = 28, d = 33, e = 10