Chapter 1, Problem 14STP

(a)

To determine

To write: an inequality that can be solved to find the minimum score he must earn on Quiz 6.

Answer to Problem 14STP

The inequality is,

  $\frac{86+79+80+85+77+x}{6}\ge 82$

Explanation of Solution

Given information:

The table as the right shows R’s scores on the first 5 math quizzes this quarter. Each quiz is worth 100 points. There will be 1 more quiz this quarter.

In order to receive a B, R must have a quiz average of 82 or better.

Calculation:

The average is easily calculated by dividing total number of points with number of quizzes taken.

In case R,

  $\frac{86+79+80+85+77+x}{6}\ge 82$

This inequality represents sum of already taken quiz scores plus $x$ which represents 6^th one that will happen divided by 6 because, there will be six quizzes total. It has to be greater or equal than 82 as said in task, So, need to put sign greater or equal than, because he has to make the minimum for B grade.

So, the inequality is,

  $\frac{86+79+80+85+77+x}{6}\ge 82$

(b)

To determine

To solve: the inequality.

Answer to Problem 14STP

The value of inequality is $x\ge 85$ .

Explanation of Solution

Given information:

The table as the right shows R’s scores on the first 5 math quizzes this quarter. Each quiz is worth 100 points. There will be 1 more quiz this quarter.

In order to receive a B, R must have a quiz average of 82 or better.

Calculation:

Consider the inequality,

  $\frac{86+79+80+85+77+x}{6}\ge 82$

Now, solve the inequality as shown,

  $\begin{array}{c}\frac{86+79+80+85+77+x}{6}\ge 82\\ 86+79+80+85+77+x\ge 6.82\\ 407+x\ge 492\\ x\ge 85\end{array}$

So, the value of inequality is $x\ge 85$ .

(c)

To determine

To find: the solution does mean.

Answer to Problem 14STP

The solution means that R has to make at least 85 points on last quiz to secure B grade

Explanation of Solution

Given information:

The table as the right shows R’s scores on the first 5 math quizzes this quarter. Each quiz is worth 100 points. There will be 1 more quiz this quarter.

In order to receive a B, R must have a quiz average of 82 or better.

Calculation:

The solution means that R has to make at least 85 points on last quiz to secure B grade.