Can anyone help me on a few percent problems? (Math 8: Chapter 5 Review-Percent)

Question

I  need help on these percent problems.

9) The following sign was on display at Hollister. ($70 $49) Determine the percent of change. 

10) A sweater that regularly sells for $110 is on sale for 30% off. What will be the new selling price of the sweater?

11) You earn a 22% commission on your sales for the month. If your total sales are $4000, what will your commission be for (the) month?

12) Ms. Lacey is the owner of a women's boutique. She wants to mark up a pair of high heels 30%. She bought them wholesale for $65. What will the new retail price be?

13) Put the following rational numbers in order from smallest to largest.

.345%, 5/4, 4.6%, 1.3, 120%, 13%

Answer 1

9)  Percent change is the amount of change with respect to the old price.  The equation is % change =

100*(new - old)/old = 100*(new/old - 1).  We then plug in 70 for old and 49 for new and get 100*(49/70-1) = -30.  The perecent change is -30%.

10.  We have the original price of $110.  We get 30% off of the original price.  So we get $110 minus the 30% of the 110 = 110 - 110*30% = 110 - 110*.3 = 77.

11.  You earn 22% of the $4,000 dollars.  A percentage is a fraction.  So you will not get the FULL $4,000 you will get only a fraction or percentage of it.  In this case it is 22%.  Whenever you see the word "of" in a percentage question like this, think multiply.  We take 4,000*22%  = 4,000*.22 = 880.  You get $880 of commission this month.

12.  This is a mark UP price not a mark DOWN price.  So we want to add the 30% to the original price.  65+65*.3 = 84.5.  Note:  We can factor out a 65 in that equation to get 65+65*.3 = 65(1+.3) = 65*1.3 = 84.5.  When marking up we can multiply the original price by (1+ % markup) because we get 100% of the original plus 30% of the original.

13.  The best way to approach this is to convert all of these to either fractions or percentages.  I will choose percentages.  We only need to get 5/4 and 1.3 to a percentage.  They are 5/4 = 125% and 1.3 = 130%.  Now just ordering from smallest to largest you get (.345%, 4.6%, 13%, 120%, 125%, 130%)

Answer 2

Hello Courtney,

 

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%)