Identify the number of sunny days in March: \(\displaystyle 13\)

Create a ratio showing sunny days in March to toal days in March (31 day month):

\(\displaystyle 13:31\)

To find the cost per ounce, divide the total cost, $1.39, by the number of ounces, 32.

\(\displaystyle \$1.39 \div 32 = \$ 0.0434375\)

This rounds to 4.3 cents per ounce.

Since a batting average is a ratio of hits to turns at bat,

\(\displaystyle \textrm{avg} = \frac{\textrm{hits }}{\textrm{at bat}}\)

Let \(\displaystyle N\) be the number of turns at bat Beltran needs to get 40 hits. Then solve for \(\displaystyle N\) in this equation:

\(\displaystyle 0.296= \frac{40}{N}\)

\(\displaystyle \frac{0.296}{1}= \frac{40}{N}\)

\(\displaystyle 0.296 \cdot N= 40\)

\(\displaystyle N = 40\div 0.296 \approx 135\)

Beltran should need 135 turns at bat.

Multiply 12 furlongs by \(\displaystyle \small \frac { 1 }{8 }\) miles per furlong, and by 5,280 feet per mile:

\(\displaystyle \small 12 \times \frac{1}{8} \times 5,280 = 7,920\) feet.

Multiply 2 miles by 5,280 feet per mile by \(\displaystyle \frac{1}{6}\) fathoms per foot:

\(\displaystyle 2 \times 5,280 \times \frac{1}{6} = 1,760\) fathoms.

The question asks to compare the number of girls to the number of boys. The ratio is \(\displaystyle 17:13\).

Since you know the ratio and the number of boys, you can set up a proportion from that ratio: \(\displaystyle \left(\frac{2}{3}=\frac{18}{x}\right)\).

Since \(\displaystyle 2\times 9=18,\) you can multiply the denominator by 9 as well. Therefore, \(\displaystyle 3\times 9=27\) and there are 27 girls in the class.

In a pet shop, there are 21 animals. Since there are 7 hamsters and 2 dogs, this leaves 12 animals that are neither a hamster nor a dog.

\(\displaystyle 21-(7+2)=12\)

Given that there are also equal numbers of cats, rabbits, and guinea pigs, this means that the remaining number of animals must be divided by 3 to find the number of each species.

\(\displaystyle 12\div3=4\)

There are 4 cats, 4 rabbits, and 4 guinea pigs.

The ratio of hamsters to guinea pigs is therefore 7:4 because there are 7 hamsters and 4 guinea pigs.

So far, there are 15 girls and, counting Mike himself, \(\displaystyle 40-15 + 1 = 26\) boys. For the ratio of girls to boys to be 3 to 2, the number of girls must be \(\displaystyle \frac{3}{2}\) times the number of boys, or

\(\displaystyle \frac{3}{2} \times 26 = 39\) girls.

15 girls have been invited already, so Mike needs to invite \(\displaystyle 39 - 15 = 24\) more girls.

So far, Sharon has invited twenty friends from school - eleven boys and nine girls. Including Sharon's cousins and Sharon herself, there are thirteen boys and ten girls. 

For there to be a two-to-one boy-to-girl ratio, Sharon must have twice as many boys as girls. She will need \(\displaystyle 10 \times 2 = 20\) boys total, so she will need to invite \(\displaystyle 20-13 = 7\) more boys.