Chapter U4.75, Problem 6E

Interpretation Introduction

Interpretation:

The number of beans in a 50 pound bag needs to be calculated given that each bean weighs 0.074 g.

Concept Introduction:

Mass is a fundamental property of an object which is representative of the amount of matter present in that object.

For small objects where the mass cannot be measured on an individual level, an average mass can be deduced by weighing the collection of similar objects and dividing by the total count.

Answer to Problem 6E

Number of beans = 306473

Explanation of Solution

Given:

Mass of one bean = 0.074 g

Total mass of all the beans in the bag = 50 pounds

Calculation:

Convert pounds to grams:

  $\begin{array}{l}1\text{ pound = 453}\text{.592 g}\\ \text{50 pounds = }\frac{\text{453}\text{.592 g}\times 50\text{ pounds}}{1\text{ pound}}=\text{22679 g}\end{array}$

Step 2: Calculate the number of beans:

  $\begin{array}{l}\text{Number of beans =}\frac{\text{Total Mass}}{\text{Mass per bean}}\\ =\frac{22679\text{ g}}{0.074\text{ g/bean}}=306,473\text{ beans}\end{array}$

Conclusion

Thus, the 50 pound bag contains 306473 beans.