Question

The table below gives the fraction of students in a class of 40 that received grades of A,B, or C on the final exam. Fill in all the missing parts of the table.

Answer 1

We have to complete the table.

We know that the total number of students will be 40. Also that the sum of the fractions of all the categories has to be equal to 1, as it represents the totality of the students.

Then, we start with the fraction of students that have grades "Below C".

We can calculate it as 1 minus the fractions for grades A, B and C:

`\begin{gathered} BC=1-\mleft(A+B+C\mright) \\ BC=1-((1)/(2)+(1)/(5)+(1)/(8)) \\ BC=1-((1)/(2)\cdot(20)/(20)+(1)/(5)\cdot(8)/(8)+(1)/(8)\cdot(5)/(5)) \\ BC=1-((20)/(40)+(8)/(40)+(5)/(40)) \\ BC=1-((33)/(40)) \\ BC=(40-33)/(40) \\ BC=(7)/(40) \end{gathered}`

We know that 7/40 of the students have grades below C.

We can now complete the column for the number of students multiplicating the fraction of students of each category by 40, the total number of students:

`\begin{gathered} N_A=(1)/(2)\cdot40=20 \\ N_B=(1)/(5)\cdot40=8 \\ N_C=(1)/(8)\cdot40=5 \\ N_(BC)=(7)/(40)\cdot40=7 \end{gathered}`

We can check the sum of the students as:

`\begin{gathered} N_A+N_B+N_C+N_(BC)=N \\ 20+8+5+7=40 \end{gathered}`

We can complete the table as: