12% of 15,000 is 0.12 * 15,000 = 1800.

8% of 15,000 is 0.08 * 15,000 = 1200; therefore in total, Mary spent 1800 + 1200 = $3000 more.

Divide Mr. Day's salary by 165 to determine how much the school pays him per day: Mr. Day makes $149 per day.  They only have to pay substitute $90 per day, saving them $59 per day. To figure out how my they save totally, multiply by 5 to get how much they save for the week Mr. Day is sick: $295. 

To find the profit percentage, you must first determine the amount of profit made on this transaction.  If the sale price was $20 and the production cost $17.50, then the profit made was: 20 -17.5 = $2.50.  The profit percentage is determined by dividing the amount of profit made by the original price, or 2.5 / 17.5 = (approx.) 0.14286 or 14.29%.

Begin by translating your problem into an equation.  What we want to ascertain is the situation when the profit equals exactly 0.  The profit and loss for a given month can be summarized by the following equation:

(Total product revenue) - (Base operating costs) - (Individual costs for products) = 0

Given our data, we can rewrite this:

15 * x - 30,000 - 5 * x = 0

Combine like terms:

10 * x - 30,000 = 0

Isolate x:

10 * x = 30,000; x = 3,000.

Therefore, the manufacturer must sell at least 3,000 items per month in order to "break even."

First, we must ascertain the original profit.  Per shirt, the retailer made 15 – 8, or $7.  Selling 300 shirts, it made a profit of $2,100.

The new price, discounted by 20% is equal to 80% of the original price, or 15 * 0.8 = $12.  This yields a profit of $4 per shirt.

To ascertain the number of sales needed to make $2,100 in profit, we must solve the following equation:

4x = 2100; x = 525 shirts

The amount of profit made on the item is 578 – 235 = $343. This is 343/235 or (approximately) 1.4596, which is 145.96% of the original price.

Set Original = O

and Discount = D

then 

D = (1 – 20%) x O = 0.80 x O

and Profit = $10 so:

10 = ((1 + 10%) x D) – D = 1.1 * D – D = 0.1D

D = 100

and O = D / 0.8 = 125

Based on the prompt, we know that the additional marketing and sales costs are 12 * 0.75 = 9; therefore, the total cost for purchase and sale is 12 + 9 = $21. To make a 50% profit, we must make 21 * 0.5, or $10.5, on the sale; thus the shirt must be sold for 21 + 10.5, or $31.5.

Let's first represent the total costs per month:

C = 25000 + 45n, where n is the number of widgets manufactured.

The profit can be represented as 60n – C or 60n – 25000 – 45n = 15n – 25000. Now, we merely have to solve this for 0 in order to find the "break even" line. 

15n – 25000 = 0 → 15n = 25000 → n = 1666.67.  We must sell a whole number of widgets, so it must be 1667.

To solve this problem we must first find out how cups he must sell without tax to break even. If each cup of lemonade costs a quarter and he has spent $20 on supplies, that means in order to make back the original $20 he spent, he must sell .  Due to this 4% business tax, he must sell 4% more in order to break even. To find that amount, we simply multiply that 4% by the number of cups he must sell without tax to break even, . He must sell an additional 3.2 cups in order to break even, however it is impossible to sell 0.2 of a cup of lemonade, therefore he must sell a minimum of 84 cups of lemonade in order to break even.