 # 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.

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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 Review Using Equations Percent as Decimal x Amount 50% = 0.5 0.5 x 300= 150

Between Ratios 100 x 3 = 300 50 x 3 = 150 Within Ratios 50 x 2 = 100 150 x 2 = 300 Proportions Have Equal…

Proportions Also Have Equal Cross Products 100v = 1,500 v = 150

A Common Mistake Total 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 Price 8% more than Coupon Price = Final price

Percent Increase (Add Amt Change) Percent Decrease (Subtract Amt Change) TaxSale TipDiscount MarkupCoupon Add or Subtract?

Core Lesson 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?

Using Between RatiosUsing Within Ratios

Using Cross Products 100x = 1,500 x = \$150

Using Equations 500 x 0.3 = \$150

Original-(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

15% 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

\$297.50 plus 7.25% Tax 297.50+(297.50x0.0725)=297.50+21.57= \$319.07 297.50 x (1 + 0.0725)= 297.50 x 1.0725 = \$319.07 Adding 7.25% is the same as 107.25% of the original amount

-35% + -15% + 7.25% = -42.75% 500 – (500 x.4275) = 500 – 213.75 = 286.25 35% off Original Price = Sale Price 15% 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 Practice After 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 Activities Tom 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?

Pretend 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?

Pretend 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 Quiz Joe’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?

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