To calculate the percentage of students who chose pizza as their favorite food, you take the number of students who chose pizza and divide by the total number of students. So first, we must calculate the total number of students. Which is simply \(\displaystyle 42+33+12+10+18=115\) total sudents.

So,

\(\displaystyle \frac{42}{115} = .365\)

Multiply our result by 100 to get into percentage form we get 36.5% 

Set up a proportion statement.

\(\displaystyle \frac{P}{100} = \frac{N}{20}\)

Solve for \(\displaystyle P\):

\(\displaystyle \frac{P}{100} \cdot 100 = \frac{N}{20}\cdot 100\)

\(\displaystyle P = 5N\)

Dividing the number by 6 is the same as multiplying it by \(\displaystyle \frac{1}{6}\). Moving the decimal point left one digit is dividing it by ten, or multiplying it by \(\displaystyle \frac{1}{10}\). The two actions together amount to multiplying the number by \(\displaystyle \frac{1}{6} \cdot \frac{1}{10} = \frac{1}{60}\).

To find its percent equivalent, multiply by 100:

\(\displaystyle \frac{1}{60} \cdot 100 = \frac{1}{60} \cdot \frac{100}{1} = \frac{1}{3} \cdot \frac{5}{1} = \frac{5}{3} = 1 \frac{2}{3}\)

The correct choice is \(\displaystyle 1 \frac{2}{3}\) % .

This is simply a matter of breaking down the problem.  10 percent of \(\displaystyle x\) is \(\displaystyle 0.1x\).

25 percent of (half of y) is 25 percent of \(\displaystyle 0.5y\) which is

\(\displaystyle .25\cdot 0.5y = \frac{y}{8}\).

Now we have these two being equal, so

\(\displaystyle \frac{x}{10} = \frac{y}{8}\)

or

\(\displaystyle 8x = 10y\)

giving

\(\displaystyle y= \frac{8x}{10} = \frac{4}{5}x\).

Finally,

\(\displaystyle \frac{y}{x}=\frac{\frac{4}{5}x}{x} = \frac{4}{5}\)

This can be most easily done by looking at the current and former price in fluts.

The current price is 1 blut, or \(\displaystyle 1 \cdot 16 \cdot 14 = 224\) fluts.

Yesterday's price was 14 gluts 10 fluts, or \(\displaystyle 14 \cdot 14 + 10 = 206\) fluts.

This represents a markup of \(\displaystyle \frac{224-206}{206} \cdot100 \approx 8.7\) percent.

If James weighs 172 pounds, and Harry weighs 80% of that, then

\(\displaystyle H = 0.8\times172\) \(\displaystyle = 137.6\) pounds. If Gary weighs 20% more than Harry, then

he is 120% Harry's weight \(\displaystyle = 1.2\times137.6=165.12\). If he loses 12 pounds,

he would weigh 153.12 or 153 pounds.

Decreasing a price by 10%, then by 20%, then by 30% is equivalent to taking 90% of a price, then taking 80% of that, then taking 70% of that. That, in turn, is equivalent to multiplying the price by 0.90, then by 0.80, then by 0.70.

For simplicity's sake, assume the initial price was $100. Then we can calculate the final price as follows:

\(\displaystyle 100 \cdot 0.9 \cdot 0.8 \cdot 0.7 = 50.4\)

The final price is $50.40, so we essentially discounted the price by $49.60, which is 49.6%.

This word problem can be written as

 \(\displaystyle x=\frac{15}{100}*80\)

Simplifying this, we get

 \(\displaystyle x=\frac{15}{100}*80 = \frac{3}{20}*80 = \frac{3}{1}*4=12\)

Out of the twenty squares, three are green; this is \(\displaystyle \frac{3}{20} = \frac{3}{20} \times 100 \% = 15\%\) of the region.

The best way to do this is to start with 100 and to calculate the final result, which will be the correct answer.

The final result will be as follows:

\(\displaystyle 100 \cdot \frac{1}{6} \div \frac{1}{7} \cdot \frac{7}{10}\)

\(\displaystyle = \frac{100 }{1}\cdot \frac{1}{6} \cdot \frac{7}{1} \cdot \frac{7}{10}\)

\(\displaystyle = \frac{100 }{1}\cdot \frac{1}{6} \cdot \frac{7}{1} \cdot \frac{7}{10} = \frac{245}{3} = 81 \frac{2}{3}\)

The final number will be \(\displaystyle 81 \frac{2}{3} \%\) of the original number.