Question

Seven out of every 8 students surveyed owns a bicycle. The difference between the number of students who own a bike and those who do not is 72. How many students were surveyed?

Answer 1

The total number of students were surveyed is 96 students

Step-by-step explanation:

         The given is,

                Seven out of every 8 students owns a bicycle

                The difference between the number of students who own a bike and those who do not is 72.

Step: 1

    Let, T - Total number of students were surveyed

           X - Students who own a bike

           Y - Students who do not bike

Step:2

          From the given,

          Ratio of Students own a bike is = $\frac{7}{8}$

          Ratio of students who do not own a bike is = $\frac{1}{8}$

Step:3

         X = Ratio of students who own bike × Total number of students

            = $\frac{7}{8}$ × T

         Y = Ratio of students who do not own bike × Total number of students

             = $\frac{1}{8}$ × T

Step:4

        From given,                     (∵ Difference is 72)

         X-Y = 72

         ( $\frac{7}{8}$ × T) - ( $\frac{1}{8}$ × T) = 72

         0.875T - 0,125T = 72

         0.75T = 72

         T = 96 students.

Step:5

        X = $\frac{7}{8}$ × T = $\frac{7}{8}$ × 96 = 84

        Y = $\frac{1}{8}$ × T = $\frac{1}{8}$ ×96 = 12

Result:

        The total number of students were surveyed is 96 students and 84 students have a own bike and 12 students do not have a own bike.