Chapter 3.7, Problem 68PPE

To determine

To solve: an absolute value equation to find the least and the greatest percent’s of voters likely to vote for the incumbent.

Answer to Problem 68PPE

The least and greatest number of voter’s likes to vote for the incumbent is: $37\le v\le 43$ .

Explanation of Solution

Given information:

The number of voter's $v$ likes to vote for the incumbent that is $40\text{\%}$ .

The poll shows a margin of error of ±3 percentage points.

Calculation:

Considering the above information:

The number of voter's $v$ likes to vote for the incumbent that is $40\text{\%}$

The poll shows a margin of error of ±3 percentage points.

Therefore,

Least percent of voters will be $|v-3|$

Greatest percent of voters will be $|v+3|$

The absolute value equation will be,

  $|v-3|\le v\le |v+3|\dots \dots (1)$

Substitute the value of $v$ to find the least percent of voters.

  $\begin{array}{cc}|v-3|& =|40-3|\\ & =\left|37\right|\\ & =37\end{array}$

Substitute the value of $v$ to find the greatest percent of voters.

  $\begin{array}{cc}|v+3|& =|40+3|\\ & =\left|43\right|\\ & =43\end{array}$

Now, substitute the value of $|v-3|$ and $|v+3|$ in the equation (1).

  $37\le v\le 43$

Hence, the least and greatest number of voter’s likes to vote for the incumbent is: $37\le v\le 43$ .