There are two steps to this problem.  First, we must calculate how much profit is made per item.  The general form of the question we are asking is, "How much is 15% of $30?"  This can be rewritten:

$\displaystyle p = 0.15 * 30 = 4.5$

Now, if you make $4.5 per item, you need to divide the total profit desired ($25,000) by $4.5:

$\displaystyle < items> = \frac{25,000}{4.5} = 5555.56$

Be careful!  You need to sell 5,556 items, NOT 5,555.  At 5,555, you will have only made $24,997.5 in profit. 

This problem implies that some original price $\displaystyle p$ was marked up by $\displaystyle 17\%$.  

This can be represented in an equation as $\displaystyle s = 1.17 * p$, where $\displaystyle s$ is the final sale price. 

Therefore, we can rewrite the equation:

$\displaystyle 37 = 1.17 * p$

Divide both sides by 1.17:

$\displaystyle p = 31.6239$

Rounding, we can say that the cost of the item is $31.62.  Subtract this from $37 to get a profit of $5.38.

$\displaystyle \\ \textup{Call \textit{c} the unit cost, then \textit{c} is also the unit profit, since 2\textit{c} is the unit price.}\\\textup{If 1,000 units are sold, 1,000\textit{c} profit is made, which we know equals \$5,000.}\\\textup{Solving the equation } 1000c=5000 \textup{ gives the desired solution } c=\$5.$

$\displaystyle 15\%$ of the total proceeds can be calculated as such:

$\displaystyle \frac{15\%}{100\%}\cdot\$3250.00=\$487.50$

If $\displaystyle 65\%$ of total income goes to overhead and expenses, that leaves $\displaystyle 35\%$ of $\displaystyle \$8,370.00$ in total profit:

$\displaystyle \frac{35\%}{100\%}\cdot\$8,370.00=\$2929.50$

If $\displaystyle \$0.55$ of every $\displaystyle \$1.00$ in sales is profit, then the profit can be calculated as $\displaystyle 55\%$ of total sales:

$\displaystyle \frac{55\%}{100\%}\cdot\$782.35=\$430.29$

The amount of profit is the money that was made in addition to the amount returned. If Jake had gotten $\displaystyle \$12.99$ back he would have not made any profit since that is what he paid for the pizza. When he sold his pizza he ended up with $\displaystyle \$16.00$ but he did not make $\displaystyle \$16.00$ in profit because he spent $\displaystyle \$12.99$ originally. His profit is calculated by

profit = total money made - total money spent

For Jake this is

$\displaystyle 8\times \$2.00-\$12.99=\$16.00-\$12.99=\$3.01$

It is possible to have a negative profit meaning Jake would have lost money. If he sold each piece for $\displaystyle \$1.00$ then his profit would be

$\displaystyle 8\times \$1.00-\$12.99=\$8.00-\$12.99=-\$4.99$

The first step is to find the total amount of profit for the month prior the added expenses. At $\displaystyle 40\%$ of total sales, this value can be calculated as such:

$\displaystyle \$14,500\cdot\frac{40\%}{100\%}=\$5,800.00$

Now that we have total profit for the month, we can divide the total profit minus the remaining profit by the original total profit to determine what percent was spent paying bills:

$\displaystyle \frac{\$5,800.00-\$523.25}{\$5,800.00}=\frac{\$5,276.75}{\$5,800.00}=0.91$

$\displaystyle 0.91\cdot100\%=91\%$

If the combined employee wages total $\displaystyle \$5,500.00/month$ , $\displaystyle 20\%$ of total income goes to rental space and $\displaystyle 33\%$ goes to cost of product, we can calculate profit as such:

$\displaystyle Total\:Profit=\$25,782.50-\$25,782.50\cdot(\frac{100\%-33\%-20\%}{100\%})-\$5,500.00$$\displaystyle Total\:Profit=\$25,782.50-\$25,782.50\cdot(\frac{47\%}{100\%})-\$5,500.00$

$\displaystyle Total\:Profit=\$25,782.50-\$12,117.78-\$5,500.00=\$8,164.72$

Billy's profit comes from the earnings of all stocks minus the amount that he initially invested.  

Find out how much Billy has spent on the fifteen stocks.  Multiply the cost of the stock by the amount he has bought.

$\displaystyle \$5 \cdot 15 = \$75$

He spent seventy five dollars on the stocks.

Find out the total amount he has sold all the stocks for.  Multiply the new price of the stocks by the amount he has sold.

$\displaystyle \$8 \cdot 15 = \$120$

Billy's profit is the difference of the earnings minus the initial price of all the stocks.  Subtract the two prices.

$\displaystyle \$120-\$75 =\$45$

Billy's profit is $\displaystyle \$45$.