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.

This basic percentage problem asks you to determine by what percentage the sum of Harry's and Gerry's share of the company is greater than ("exceeds") Izzy's share. Harry's and Gerry's share's are equal, and the sum is 60% of the company (100% – Izzy's 40% = 60%). 60% is 50% greater than 40% (0.40 * 1.5 = 0.60). Examinees may be tempted to go too far with the problem and mistake their task by finding how much greater Izzy's share is than either Harry's or Gerry's. Be careful to read instructions and translate keywords appropriately.

You may think the answer is 20% (60% – 40%), but this is the difference in terms of total shares in the company, not in terms of Izzy's shares, which is what the question is asking.

The circumference of a circle increases linearly with its radius.  Therefore, an increase in circumference from 20 to 45 represents an increase of (45 – 20) / 20 = 25 / 20 = 125% increase.  This means that if the radius was r, it is now r + 1.25r = 2.25r.

Now, the original area, supposing r as our radius, would be πr²

The new area would be π(2.25r)² = 5.0625πr²

The percent change would be: (5.0625πr² - πr²) / πr²  = (4.0625πr²) / πr² = 4.0625 or 406.25%

For this problem, pay attention only to the values between 2002 and 2006 - each of which is 17 (thousand) and 22 (thousand). Note that the decrease within this range does not need to be accounted for, as the question asks only for values relative to 2002 and 2006. 

To calculate percent change, take it as a fraction: 22/17 = 1.294; this represents approximately 129% of the actual value or a 29% increase in sales across these 4 years.

In the problem, 150% of 6 represents the change in the value, not the new value. Percent "greater than" is a key phrase that refers to percent change. Therefore, 9, or 150% of 6, is how much 6 increases. The answer is 6 + 9 = 15.

Formula: Original * (1 + percent increase/100) = New

6(1 + 1.50) = 15

If book sales were 100/day then an increase by 50% means they would reach 150/day (by the end of April). A decrease at that point means a 50% decrease in 150/day which would lower book sales to 75/day. Thus sales were higher at the beginning of April than at the end of May.