9) The formula for finding percentage is: x% = ((original - new)/original)*100. This formula will give you the exact percent discount. So in this case it would be: ((70-49)/70)*100 = 30%. This means that Hollister is providing a 30% discount to their customers.
10) Using the formula from above, we know x% = 30; however we do not know the new price. So, we can rearrange the same formula to find the new price: new = -(((x%/100)*original)-original). In this case the new price would be: -(((30/100)*110)-100) = 77. This means that the new price is $77.
11) Because we are no longer looking for a discount we can take away the portion of subtracting the original price. For example, anytime finding the percent value of a number, we simply use the following formula: new = (x%/100)*original. However, when finding the amount discounted, we subtract this amount from the original value as in problems 9 & 10. In this case, the commission on a sale of $4,000 at 22% will be calculated as such: new = (22/100)*4000 = $880. The commission the sales man will receive is $880.
12) Now this one is a bit tricky because instead of finding the discounted value we will find a value that the percent represents and add it to the original value. This is because Ms. Lacey wants to mark up the price for a 30% profit. So using the formula in problem 11 we find the value that 30% of $65 represents: (30/100)*65 = 19.50. This means that Ms. Lacey wants to mark up $19.50 above the amount of $65. So we will simply add 65+19.50 and get $84.50. Ms. Lacey should sell the pair of high heels for $84.50 for a 30% profit.
13) The simplest way to do this kind of problem is by increasing percent as if they were represented on an axis or on a number line from 0 to infinity. However, '5/4' is not represented as a decimal value. So to do that we can simply divide 5 by 4: 5/4 = 1.25. Now, a percent is represented by equal parts of 100. Therefore, multiply 1.25 by 100 and this means 125%. Now we can put all the numbers in order: 0.345%, 1.3%, 4.6%, 13%, 120%, 5/4 (125%)