A library contains 67,982 books. The children's section represents 1/3 of the total books. Of the remaining books, 75% are fiction. How many books are in the non-fiction section?

First convert 25% to decimal as

25% =\(\frac{25}{100}\)= 0.25

Now, 0.25 = 0.25

Use the relation 1 gallon= 128 fluid ounces to convert between gallons and ounces. Then,

\(576\ fluid\ ounces\ast\frac{1 gallon}{128 fluid ounces}=4.5 gallons\)

Convert the mixed fractions into improper fractions as:

\(7 7/10=\frac{\left(10\ast7\right)+7}{10}=\frac{70+7}{10}=\frac{77}{10}\)

\(3 4/5=\frac{\left(5\ast3\right)+4}{5}=\frac{15+4}{5}=\frac{19}{5}\)

Now, subtract the improper fractions as:

\(\frac{77}{10}-\frac{19}{5}=\frac{77-19\left(2\right)}{10}=\frac{77-38}{10}=\frac{39}{10}\)

As a mixed fraction\(\frac {39}{10}\) becomes\(3 \frac {9}{10}\)

The number of packets of a balloon to purchase is evaluated as follows

\(16\ children\ast\frac{15 balloons}{1 child}\ast\frac{1 packet}{50 balloons}=\frac{24}{5}=4.8 packets\)

Approximating 4.8 to 5, the mother will have to buy 5 packets of balloons.