Chapter 11.1, Problem 43CCR

To determine

To find: What is the lowest score he can receive on his sixth quiz to obtain this average

Answer to Problem 43CCR

Tobias will have to score at least $98$ points on his sixth quiz to obtain an average of $88$

Explanation of Solution

Given information:

Tobias’ average for five quizzes $=86$

He wants to have an average of at least $88$ for six quizzes.

Given

Tobias’ average for five quizzes $=86$

First we need to find total number of points Tobias scored on the first $5$ quizzes

Average $=\frac{T}{n}$

Where

  $T=$ Total number of points

  $n=$ Number of quizzes

On substituting values

We get

  $\begin{array}{l}\Rightarrow 86=\frac{T}{5}\\ \Rightarrow T=86\times 5\\ \Rightarrow T=430\end{array}$

Therefore,

Total number of points for $5$ quizzes $=T=430$

Let $x$ be the lowest score Tobias can receive on his sixth quiz to obtain on average of $88$

Average $=\frac{T}{n}$

  $\begin{array}{l}\Rightarrow 86=\frac{T}{5}\\ \Rightarrow T=86\times 5\\ \Rightarrow =T=430\\ 88=\frac{430+x}{6}\\ \Rightarrow 430+x=88\times 6\\ \Rightarrow 430+x=528\\ \Rightarrow x=528-430\\ \Rightarrow x=98\end{array}$

Therefore,

Tobias will have to score at least $98$ points on his sixth quiz to obtain an average of $88$