Chapter 12.3, Problem 2P

a.

To determine

To find: The minimum grade required in the last test in order to achieve an average of $90$ .

Answer to Problem 2P

  $89$

Explanation of Solution

Given information:

A student has gotten $80,93\text{ and 91}$ grades in his tests. An average of $88$ is desired.

Calculation:

Let $x$ grade is required in fourth test.

  $\begin{array}{l}\text{So, }\frac{80+93+91+x}{4}=88\\ \Rightarrow \frac{264+x}{4}=88\\ \Rightarrow 264+x=352\\ \Rightarrow x=352-264\\ \Rightarrow x=89\end{array}$

Hence, student would need minimum $89$ grades in fifth exam to achieve an average of $88$ .

b.

To determine

To find: If it is possible to achieve average of $92$ .

Answer to Problem 2P

No.

Explanation of Solution

Given information:

A student has gotten $80,93\text{ and 91}$ grades in his tests. An average of $92$ is desired.

Highest marks in an exam is $100$ .

Calculation:

Let $x$ grade is required in fourth test.

  $\begin{array}{l}\text{So, }\frac{80+93+91+x}{4}=92\\ \Rightarrow \frac{264+x}{4}=92\\ \Rightarrow 264+x=368\\ \Rightarrow x=368-264\\ \Rightarrow x=104\end{array}$

Since highest marks of an exam is $100$ . Hence, it is not possible to achieve an average of $92$ .