Lesson 19 Proportionality Percent Applications.

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Presentation transcript:

Lesson 19 Proportionality Percent Applications

Warm-Up Solve the proportion: . Identify the percent of change as an increase or a decrease. Find the percent of change. 50 to 40 18 to 20

Target: Solve problems involving mark-ups, discounts, tips and taxes. Percent Applications Target: Solve problems involving mark-ups, discounts, tips and taxes.

Vocabulary Mark-up: The increase in the price of an item. Discount: The decrease in the price of an item. Sales Tax: An amount added to the cost of an item. The amount added is a percent of the original amount as determined by a state, county or city.

Example 1 A pawn shop owner buys a ring for $75 and sells it at an 80% mark-up. Find how much the ring sold for. Method 1: Proportions Method 2: Percent Equation x = 80%·75 x = 0.8·75 x = 60 Method 3: Percent of Increase The markup is $60. The total price is 60 + 75 = $135.

Example 2 Sesily found an outfit that is 20% off the original price of $68. Find the discounted price of the outfit. Method 1: Proportions Method 2: Percent Equation x = 20%·68 x = 0.2·68 x = 13.6 Method 3: Percent of Increase The discount is $13.60. The sale price is 68 – 13.60 = $54.40.

Example 3a Leah bought a new stereo in Seattle, Washington for $250. Find the actual amount she paid at the checkout if she was charged the state sales tax of 6.5%. Find 6.5% of $250. Use the percent equation. x = 0.065·250 x = 16.25 Add the tax to the total. 16.25 + 250 = $266.25 Leah would pay $266.25 for the stereo.

Example 3b Leah bought a new stereo in Seattle, Washington for $250. Find the actual amount she paid at the checkout if she was charged the city and state tax combined of 8.45%. Find 8.45% of $250. Use the percent equation. x = 0.0845·250 x = 21.125 Round to nearest cent. x ≈ 21.13 Add the tax to the total. 21.13 + 250 = $271.13 Leah would pay $271.13 for the stereo.

Example 4 Roy paid $8.05 for an antique model truck. It was on sale for 30% off. Find the original price of the model truck. Roy paid 100% – 30% = 70% of the price. Let x = original price. Write a proportion. Use cross products to solve. 70x = 805 x = 11.5 The model truck was originally $11.50.

Exit Problems Find each selling price. original price: $20.00 percent of markup: 15% original price: $16.00 percent of discount: 30%

Communication Prompt What is something that has had a percent increase of more than 100% in your lifetime?