Chapter 1, Problem 38SGR

To determine

To Find: The length of the shortest and the longest ribbon.

Answer to Problem 38SGR

Thelongest piece of the ribbon is $\frac{13}{16}\text{yard}$ and the shortest piece is $\frac{11}{16}$ yards.

Explanation of Solution

Given:

Marcos is cutting ribbons for a craft project. Each ribbon needs to be $\frac{3}{4}$ yard long.

Each piece is always within plus or minus $\frac{1}{16}$ yard.

Calculation:

Consider the piece of the ribbon measured by $x$ . Then the absolute equation is written as,

  $\left|x-\frac{3}{4}\right|=\frac{1}{16}$

Solve the above equation as,

  $\begin{array}{l}x-\frac{3}{4}=\pm \frac{1}{16}\\ x=-\frac{1}{16}+\frac{3}{4},\frac{1}{16}+\frac{3}{4}\\ x=\frac{11}{16},\frac{13}{16}\end{array}$

Thus, the longest piece of the ribbon is $\frac{13}{16}\text{yard}$ and the shortest piece is $\frac{11}{16}$ yards.