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Section 6C –Commission, Interest, Tax, Markup and DiscountIn the last section, we looked at percent conversions and solving simple percent problems witha proportion. We are now going to look at some more complicated percent applications.CommissionMany people work on commission. In a general sense, you get paid a percentage of what yousell. The more you sell, the more money you make. Usually people have a set commission rate(percent) that they will be paid. The formula for commission is C T r where C is theamount of commission they are paid, T is the total sales and r is the commission rate (percent).As with most of these formulas involving percent, we need to be sure to convert the percent toeither a fraction or decimal, before plugging in for r.For example, look at the following commission problem. Marsha gets paid 12% of all makeupshe sells. She made a total of 216 this week from commission. What was the total sales ofmakeup for the week? Like with any formula, plug in what you know and solve for what youdon’t know. We first must convert the 12% into a fraction or decimal. 12% 12 100 0.12 ,so we will plug in 0.12 for r and 216 for C and then solve for T.C T r216 T (0.12)100(216) 100(0.12T )21600 12T21600 12 T 1212 1800 TSo Marsha sold 1800 in makeup this week in order to make the 216 in commission.Simple InterestSimple Interest is an important concept for everyone to know. It a big part of financial stabilityand is vital to understanding savings accounts. The formula for simple interest is I P r twhere P is the principal (amount invested), r is the interest rate (percent), and t is time in years.Let’s look at an example. Jerry deposited 3500 into a simple interest account. He was able toearn 122.50 in interest after 6 months (1/2 year). What was the interest rate the bank used?Write your answer as a percent.169

Again, plug in what we know and solve for what we do not know. We know I 122.5, P 3500and t ½ . Now let’s solve for r.I P r t122.5 3500 r 12122.5 1750r1122.51750 r175017500.07 rNow the interest rate is not written as a percent. Do you remember how to convert a decimalinto a percent? Remember, if you see the percent symbol, divide by 100, but if you do not seethe percent symbol and you want to put one on, multiply by 100.So r 0.07 0.07 x 100% 7%So Jerry’s bank gave him a 7% interest rate.Try the following example problems with your instructor. Pay close attention to see if you needthe commission or simple interest formula.Example 1: Jimmy sells cars and is paid a commission for the cars he sells. In one day he soldthree cars for a total of 43,000 and was paid a commission of 1720. What is Jimmy’scommission rate? Write your answer as a percent.Example 2: Rick invested 4,000 into a bank account that earns 6% simple interest. How longwill it take Rick to make 720 in simple interest?(This section is from Preparing for Algebra and Statistics , Third Editionby M. Teachout, College of the Canyons, Santa Clarita, CA, USA)This content is licensed under a Creative CommonsAttribution 4.0 International license170

Taxes and MarkupMost people living in the U.S. have to pay taxes. Whether you buy coffee or a car, you need topay taxes, but how do taxes work? Taxes in CA can vary depending on where you are. Someareas have a tax rate of 9.25% and other areas have a tax rate of 8.5%. So basically a tax is apercent of increase. The store multiplies the percent times the price of the item to calculatethe tax. Then it adds the tax onto the price to get the total you have to pay. A commonformula for calculating the total with taxes included is T A rA where T is the total paid, A isthe original amount of the item before taxes and r is the tax rate percent for the area you livein.Let’s look at an example. Suppose an electric shaver costs 64 at the store. When you go topay, the total is 69.92. What is the tax rate? Write your answer as a percent.Since we know the total T 69.92 and the amount A 64, we can solve for r in the formula.Remember, we will need to convert our answer into a percent by multiplying by 100.T A rA69.92 64 r (64)69.92 64 64r 64 645.92 64r15.9264 r 64640.0925 rNotice a few things. First 64 64r is not 128r. Remember these are not like terms. So we needto bring the r terms to one side and constants to the other. This is why we subtract the 64 fromboth sides. The 5.92 was actually the amount of tax they charged. After solving we got ananswer of r 0.0925 and converting that into a percentage we get r 0.0925 x 100% 9.25%.So in the electric shaver problem, we were in an area that charges a 9.25% sales tax.Another type of problem that uses the same percent of increase problem is a markup. Amarkup is when a store buys an item from a manufacturer for a certain cost and then sells it toyou for a higher price. For example some stores have a 10% markup rate. Meaning whateverthe cost of the item, they add an additional 10% onto the price before selling it. This is howstores make money. Since it is a percent of increase, a markup also uses the formula T A rAwhere A is the amount before the markup and T is the total after the markup and r is themarkup rate (percent).171

Look at the following problem. A store bought a tennis racquet from the manufacturer. If theyhave a standard 15% markup policy on all items, and they sold the racquet for 72.45 aftermarkup, what was the cost of the racquet from the manufacturer? We first see that we aregiving the markup rate at 15%. Again make sure to convert that into a fraction or decimalbefore plugging in for r. 15% 15 100 0.15 r. So we will plug in T 72.45 and r 0.15 andsolve for A.T A rA72.45 A 0.15 A72.45 1.15 A100(72.45) 100(1.15 A)7245 115 A17245115 A 11511563 ANotice a few things. First that A is the same as 1A, so since the 1A and the 0.15A are like terms,we can add them and get 1.15A. Also a common technique to eliminate decimals is to multiplyboth sides of the equation by a power of 10, which in this case was 100. So the store boughtthe tennis racquet originally for 63 and then sold it to us for 72.45.DiscountOur final percent application is discount and sale price. We have all been in stores thatsometimes say 25% off or 50% off sale. We know that the sale price is lower than the regularprice, but how does a discount work? A discount is really a percent of decrease. The storemultiplies 25% times the price of the item. This is called the discount. Then the store subtractsthis amount from the price of the item, before charging you. A common formula used indiscount problems is T A – rA. Notice this is very similar to the tax or markup formula but it isa decrease (-) instead of an increase ( ). In this formula, A is the amount of the item before thesale and T is the total price of the item after the discount and r is the discount rate (percent).Let’s look at an example. A car has a regular price of 18000 and is on sale for 14,400. Whatwas the discount rate? Write your answer as a percent.Plugging into our equation we see that the amount before the sale was A 18000 and the totalprice after the sale was T 14400. Plug in and solve for r. Again we will have to convert r into apercent by multiplying by 100.172

T A rA14400 18000 r (18000)14400 18000 18000r 18000 18000 3600 18000r1 3600 18000 r 18000 180000.2 rNotice a few things. The 18000 is the A not the T. In sale price problems the price decreases sothe large amount is the price before the sale. The 14400 is the sale price or the amount afterthe sale. The -3600 indicates that there was a 3600 discount. Our answer as a percent isr 0.2 0.2x100% 20%. So the car was being sold at a discount of 20%.Try the following examples with your instructor. Be sure to use the formulas T A rA for taxand markup and the formula T A – rA for discount problems.Example 3: Rachael lives in an area with a 9.5% sales tax and bought a blouse for 45.99 withtax included. What was the price of the blouse before tax?Example 4: A clothing store bought some jeans from the manufacturer for 16 and then soldthem to their customers for 22.40. What was the markup rate? Write your answer as apercent.173

Example 5: Juan bought a rosebush to plant in his backyard. The rosebushes were on sale for35% off. If the sale price that Juan paid was 15.60, what was the price of the rosebush beforethe sale?Practice Problems Section 6C (Don’t forget to convert given percentages rates (r) into adecimal before plugging into the formulas.)Commission Problems ( C T r )1. Tina sells software and is paid a 20% commission on all she sells. If she sold a total of 8000worth of software in one month, how much commission did she make from the sale?2. Maria sells hair products at the mall and is paid a commission on what she sells. If she sold atotal of 860 in hair products and was paid a commission of 154.80, what is her commissionrate? Write your answer as a percent.3. Jim sells homes and earns a 4% commission on all he sells. If he made a commission of 19,000 on one home he sold, what was the total price of the house?4. Rachel sells cars and is paid a commission on what she sells. If she sold a total of 66,400worth in cars and was paid a commission of 4,648, what is her commission rate? Write youranswer as a percent.5. Jim sells paintings and earns a 6.5% commission on all he sells. If he made a commission of 279.50 on one painting he sold, what was the total price of the painting?Simple Interest Problems ( I P r t )6. Kai invested 3000 into some stocks that yielded a 6.8% interest rate. How much simpleinterest did she make after 2 years?7. Simon invested 2600 into a simple interest account for 2 years. If the account yielded 234at the end of two years, what was the interest rate? Write your answer as a percent.174

8. Elena invested some money into a bond account that yielded 375 in interest at the end of 1year. If the interest rate was 3%, how much did she originally invest?9. Yessica invested 5000 into a simple interest savings account that yields 6.5% simpleinterest. How many years will it take for her to make 1300 in simple interest?10. Simon invested 3500 into a simple interest account for 2 years. If the account yielded 385 at the end of two years, what was the interest rate? Write your answer as a percent.Tax and Mark-up Problems T A rA 11. Tim bought a washing machine for a total of 651 with tax included. What was the price ofthe washing machine before tax if Tim lives in an area with an 8.5% sales tax rate?12. Julie wants to buy an iPhone that costs 120 before tax. If Julie lives in an area with a9.25% sales tax, what will be the total price of the iPhone with tax included?13. Lianna bought a turtleneck sweater for 19.71 with tax included. If the price of the sweaterbefore tax was 18, what is the sales tax rate in Lianna’s area? Write your answer as a percent.14. Wade works for a store that sells computers and computer parts and has a 20% markuppolicy. If they bought a computer from the manufacturer for 790, how much will they sell itfor after the markup?15. Patricia works for a clothing store. If the store buys its sweatshirts from the manufacturerfor 19 and then sells them for 28.50, what is the stores markup rate? Write your answer as apercent.Sale Price Problems T A rA 16. A bicycle that regularly sells for 350 is on sale for 25% off. What will the sales price be?17. If Oscar bought some patio furniture that regularly sells for 275 on sale for 192.50 , whatwas the discount rate? Write your answer as a percent.18. Tyrone bought a shed to put in his backyard. If the shed was on sale for 20% off and thesale price was 360, what was the regular price of the shed before the sale?19. Tara bought a necklace that regularly sells for 450 on sale for 315, what was the discountrate? Write your answer as a percent.20. Rick bought a book on sale for 40% off and the sales price was 30. What was the regularprice of the shed before the sale?175