How do you compute successive percents?

For example:Eli bought a computer that was on sale for 30% off its original price of $500. Eli also used a coupon for a 15% discount

on the sale price. The tax rate was 7.25%. How much did Eli pay for the

computer?

In this lesson you will learn how to compute successive

percentages by using proportions and equations.

Let’s ReviewUsing Equations

Percent as Decimal x Amount

50% = 0.5

0.5 x 300=150

Let’s Review

Between Ratios

100 x 3 = 30050 x 3 = 150

Within Ratios 50 x 2 = 100

150 x 2 = 300

Proportions Have Equal…

Let’s Review

Proportions Also Have Equal Cross Products

100v = 1,500v = 150

A Common MistakeTotal Percent Change = Sum of Percent Changes

25% off sale, 10% off sale price coupon, 8% Tax

-25% + -10% + 8% = -27% 25% off Original Price = Sale Price

10% off Sale Price = Coupon Price8% more than Coupon Price = Final price

A Common Mistake

Percent Increase(Add Amt Change)

Percent Decrease(Subtract Amt

Change)Tax SaleTip Discount

Markup Coupon

Add or Subtract?

Core LessonEli bought a computer that was on sale for 30%

off its original price of $500. Eli also used a coupon for a 15% discount on the sale price. The tax rate was 7.25%. How much did Eli pay for the

computer?

Core Lesson

Using Between Ratios Using Within Ratios

Core LessonUsing Cross Products

100x = 1,500

x = $150

Core LessonUsing Equations

500 x 0.3 = $150

Core LessonOriginal-(Original x %off) = Sale Price

500-(500x0.3) = 500-150 = $350

500 x (1—0.3) = 500 x 0.7 = $350

30% off is the same as 70% of original amount

Core Lesson15% coupon off of $350

350 – (350 x 0.15) = 350 – 52.50 = $297.50

350 x (1—0.15) = 350 x 0.85 = $297.50

Core Lesson$297.50 plus 7.25% Tax

297.50+(297.50x0.0725)=297.50+21.57=

$319.07297.50 x (1 + 0.0725)= 297.50 x 1.0725 =

$319.07

Adding 7.25% is the same as 107.25% of the original amount

Core Lesson-35% + -15% + 7.25% = -42.75%

500 – (500 x .4275) = 500 – 213.75 = 286.25

35% off Original Price = Sale Price15% off Sale Price = Coupon Price

7.25% more than Coupon Price = Final price

$286.25 versus $319.07

In this lesson you have learned how to calculate successive

percentages by using a proportions and equations.

Guided PracticeAfter eating at your favorite restaurant, you know the bill before tax is $52.60 and the sales tax is 8%. You decide to leave a 20% tip for the waiter based on the pre-tax amount. How much should you leave for the waiter? How much will the bill be with tax? How much will you spend in total?

Extension ActivitiesTom has raised $2,000 and started a charity to provide book bags of school supplies for poor children. Tom packs each bag with 2 notebooks and 10 pencils. At the store the original price of 1 book bag is $22.50, of 1 notebooks is $3.25, and of 1 pencil is $0.19. However, all items are on sale for 30%. Tom also receives an additional 10% discount off of the sale price, because the products are for a charity. Tax is 8.25%. How many book bags can Tom make?

Extension ActivitiesPretend that you deposited $500 in 3 different savings accounts at three banks. Bank A provides customers with 2% interest on their investments per month. Bank B provides 5% and Bank C offers 7%. Create a table of how much money that you will have in each account at the end of each month. How do the amounts compare after 1 year? What about after 5 years?

Extension ActivitiesPretend that had a job that earned 5% commission of your sales. How much would you need to sell to earn one million dollars pre-tax? Your state government deducts 12% from your earnings. The federal government deducts 6.5% from your earnings. How much would you need to sell to earn one million dollars post-tax?

Quick QuizJoe’s bill at the restaurant was $52.70. He decided to leave his server 15% tip on the pre-tax bill. The tax rate is 8%. How much of a tip will he leave? How much is the bill after tax? How much will he spend in total?

A $750 computer is on sale for 25% off. You also have a coupon for 10% off the sale price. Tax is 8%. How much will the computer cost?