1. Lesson 19
Proportionality
Percent Applications

2. 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

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

4. 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.

5. 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 = $135.

6. 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 $ The sale price is 68 – = $54.40.

7. 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 = $266.25
Leah would pay $ for the stereo.

8. 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 = ·250
x =
Round to nearest cent x ≈ 21.13
Add the tax to the total = $271.13
Leah would pay $ for the stereo.

9. 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 x = 805
x = 11.5
The model truck was originally $11.50.

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

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