A nursing school enrolls 89 students, and 7 out of 8 are female. What percentage of the class is female?

The proportion equation of the ratio 100:2=60:X is

\(\frac{100}{2}=\frac{60}{X}\)

Cross-multiply to find the value of X

\(100X=2\ast60\)

\(100X=120\)

Divide both sides by 100

\(\frac{100X}{100}=\frac{120}{100}\)

\(X=1.2\)

The value of X is 1.2

We use dimension analysis to find the number of diapers the child uses in a year. In a day, the mother uses 6 diapers and a year has 365 days. Then, the number of diapers in one year becomes:

\(365\ days\ast\frac{6\ diapers}{1\ day}=2190\ diapers\)

In a year, the child will use 2190 diapers.

First convert the mixed fractions into improper fractions as follows

1 3/5=\(\frac{\left(5\ast1\right)+3}{5}=\frac{5+3}{5}=\frac{8}{5}\)

2 7/9=\(\frac{\left(9\ast2\right)+7}{9}=\frac{18+7}{9}=\frac{25}{9}\)

Then, multiply the fractions

1/2 x 1 3/5 x 2 7/9=\(\frac{1}{2}\ast\frac{8}{5}\ast\frac{25}{9}=\frac{20}{9}\)

As a mixed fraction 20/9 becomes 2 2/9

The number of packets of a balloon the mother should purchase is evaluated as follows

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

The mother will have to purchase 5 packets of balloons.