Chapter 1.4, Problem 47E

a.

To determine

To write: and solve an absolute value equation to find the least and greatest percent of students who could be in favor of year-round school.

Answer to Problem 47E

  $\left|x-32\right|=5$

  $27\%,37\%$

Explanation of Solution

Let x denotes the percent of students who could be in favor of year-round school.

Now, it is given that the percent of students who could be in favor of year-round school is 32% with an error of $\pm 5\%$ .

Thus, the absolute value equation representing the given solution is:

  $\left|x-32\right|=5$

It is equivalent to:

  $x-32=\pm 5$

Now,

  $\begin{array}{c}x-32=5\\ x=32+5\\ x=37\end{array}$

Or

  $\begin{array}{c}x-32=-5\\ x=-5+32\\ x=27\end{array}$

Check:

  $\begin{array}{c}\left|37-32\right|=5\\ \left|5\right|=5\\ 5=5\end{array}$

And

  $\begin{array}{c}\left|27-32\right|=5\\ \left|-5\right|=5\\ 5=5\end{array}$

Both the statements are true.

Conclusion:

Thus, the least and greatest percent of students who could be in favor of year-round school are 27% and 37% respectively.

b.

To determine

if the statement, “ $\frac{1}{3}$ of the student body is in favor of year-round school” conflict with the survey data.

Answer to Problem 47E

No it does not conflict the survey data.

Explanation of Solution

Since $\frac{1}{3}=33\frac{1}{3}\%$ falls in the range of possible values 27% to 37% as obtained in part (a), so it is appropriate to say that, $\frac{1}{3}$ of the student body is in favor of year-round school.