Chapter 1, Problem 82A

To determine

To Calculate: The number of shorts which are equal to one long.

Answer to Problem 82A

  $1\text{longs}\text{=161}\text{.9}\text{shorts}$

Explanation of Solution

Given:

  $\begin{array}{l}1.2\text{3}\text{longs}=23.0\text{mediums}\\ \text{74}\text{.5}\text{mediums}=645\text{shorts}\end{array}$

Calculations:

First find, number of shorts in 1 medium.

Divide both sides by $74.5$ .

  $\begin{array}{l}\text{74}\text{.5}\text{mediums}=645\text{shorts}\\ \text{1}\text{medium = }\frac{645}{\text{74}\text{.5}}\text{shorts}\end{array}$

Then, write $23.0\text{mediums}$ in terms of shorts.

  $1.2\text{3}\text{longs}=23.0\text{mediums}\times \frac{645}{\text{74}\text{.5}}\text{shorts/mediums}$

Divide both sides by 1.23.

  $\begin{array}{c}1\text{longs}=\frac{1}{1.23}\times 23.0\text{mediums}\times \frac{645}{\text{74}\text{.5}}\text{shorts/mediums}\\ 1\text{long =161}\text{.9}\text{shorts}\end{array}$

Conclusion: $1\text{long}\text{=161}\text{.9}\text{shorts}$