Question

eighty members of a bike club were asked whether they like touring bikes and whether they like mountain bikes. a total of 70 like touring bikes, 47 like mountain bikes, and 5 do not like either. types of bikes 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?

Explanation:

Step1: Find the value of \(e\)

The total number of members is \(80\). The number of members who like touring bikes is \(70\). Using the formula \(e=\text{Total}-\text{Likes Touring Bikes}\), we have \(e = 80 - 70=10\).

Step2: Find the value of \(b\)

We know that \(e\) (the number of members who do not like touring bikes) is \(10\). The number of members who do not like either (and are in the "Does Not Like Touring Bikes" and "Does Not Like Mountain Bikes" cell for non - touring) is \(5\). So, \(b=e - 5\). Substituting \(e = 10\), we get \(b=10 - 5 = 5\).

Step3: Find the value of \(a\)

The number of members who like mountain bikes is \(47\). Since \(a + b=47\) (from the row "Likes Mountain Bikes"), and \(b = 5\), then \(a=47 - b\). Substituting \(b = 5\), we have \(a=47-5 = 42\).

Step4: Find the value of \(c\)

The number of members who like touring bikes is \(70\). Since \(a + c=70\) (from the column "Likes Touring Bikes"), and \(a = 42\), then \(c=70 - a\). Substituting \(a = 42\), we get \(c=70 - 42=28\).

Step5: Find the value of \(d\)

The total number of members is \(80\). The number of members who like mountain bikes is \(47\). So, \(d=\text{Total}-\text{Likes Mountain Bikes}\). Substituting the total number of members \(80\) and the number of members who like mountain bikes \(47\), we have \(d = 80 - 47=33\).

Answer:

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