Chapter 1.5, Problem 5PPC

Interpretation Introduction

Interpretation:

The total weight of the given orange boxes has to be determined according to the given data.

Concept introduction:

Certain conversion factors are used to do unit conversions.

Average weight can be expressed in different units like kilogram, gram, pounds, ounces etc.

General conversions are:

$\begin{array}{l}\text{1}\text{kilogram}\text{=}\text{1000}\text{g}\\ \text{1}\text{ounce}\text{=}\text{0}\text{.06}\text{pounds}\text{=}\text{0}\text{.06}\text{lb}\\ \text{1}\text{pound}\text{=}\text{16}\text{ounces}\end{array}$

Answer to Problem 5PPC

The total weight of the given five orange boxes is $\text{2}\text{.192}\text{×}{\text{10}}^{\text{2}}\text{lb}$

Explanation of Solution

Given that there are 100 oranges in a box and the average weight of an orange is $\text{7}\text{.2}\text{ounces}$

The average weight of boxes in which oranges are packed is $\text{3}\text{.2}\text{pounds}$

We have to find out total weight of five of these 100 orange boxes.

First we have to convert ounces to pound. For this general unit conversion has to be used.

$\begin{array}{l}\text{1}\text{ounce}\text{=}\text{0}\text{.06}\text{pounds}\text{=}\text{0}\text{.06}\text{lb}\\ \text{7}\text{.2}\text{ounce}\text{=}\frac{\text{0}\text{.06}\text{lb}\text{×}\text{7}\text{.2}\text{ounce}}{\text{1}\text{ounce}}\\ \text{7}\text{.2}\text{ounce}\text{=}\text{0}\text{.432}\text{lb}\end{array}$

$\begin{array}{l}\text{Average}\text{weight}\text{of}\text{an}\text{orange}\text{=}\text{0}\text{.432}\text{lb}\\ \text{Average}\text{weight}\text{of}\text{100}\text{oranges}\text{=}\text{0}\text{.432}\text{lb}\text{×}\text{100}\\ \text{=}\text{43}\text{.2}\text{lb}\end{array}$

Given that average weight of the boxes in which oranges are packed is $\text{3}\text{.2}\text{pounds}$

$\begin{array}{l}\text{Average}\text{weight}\text{of}\text{one}\text{box}\text{=}\frac{\text{3}\text{.2}}{\text{5}}\\ \text{=}\text{0}\text{.64}\end{array}$

$\begin{array}{l}\text{Total}\text{weight}\text{of}\text{one}\text{orange}\text{box}\text{which}\text{contain}\text{100}\text{oranges}\text{=}\text{43}\text{.2}\text{+}\text{0}\text{.64}\\ \text{=}\text{43}\text{.84}\text{lb}\\ \text{Total}\text{weight}\text{of}\text{five}\text{orange}\text{boxes}\text{which}\text{contain}\text{100}\text{oranges}\text{=}\text{43}\text{.84}\text{×}\text{5}\\ \text{=}\text{2}\text{.19}\text{×}{\text{10}}^{\text{2}}\text{lb}\end{array}$

Conclusion

Total weight of the given five 100 orange boxes are calculated and found as $\text{2}\text{.192}\text{×}{\text{10}}^{\text{2}}\text{lb}$