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Percent of Change

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**The ratio of the amount of increase or decrease to the original amount**

Percent of Change: The ratio of the amount of increase or decrease to the original amount It is an increase when the new amount is larger than the original and a decrease when the new amount is smaller than the original. To find the percent of change, use the following proportion: Percent of change: Amount of increase or decrease = % Original Amount

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**Find the percent of change**

(be sure to label your answer as an increase or decrease). Examples: Original amount: 20 Original amount: 40 New amount: New amount: 10 Percent of change= Percent of change=

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**Identify the percent of change as an increase or decrease**

Identify the percent of change as an increase or decrease. Then find the percent of change. 1. Original: 45 New: 75 2. Original: 100 New: 42 3. Original: 58 Answer: Increase 66.7% Decrease 58% Increase 29.3%

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**A CD's original price was $12.99. It is now on sale for $10.99. **

Try This! A CD's original price was $12.99. It is now on sale for $10.99. What is the percent of change? Answer: 15.4% decrease

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**A student's first test grade was 60. The second test grade was an 85. **

Try This! A student's first test grade was 60. The second test grade was an 85. What was the percent of change? Answer: 41.7% increase

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41 The number of students who attended FHS in 2010 was In 2011, 1380 students attended
FHS. What was the percent of change in student enrollment? Answer: 1.8% decrease

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**Find the percent of change. Original price: $80 Sale price: $50**

43 Find the percent of change. Original price: $80 Sale price: $50 Answer: 37.5% decrease

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44 A stereo, originally priced at $360, is on sale for $200. What is the percent of change? Answer: 44.4% decrease

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**There are situations when the percent of change is going to be a decrease. Examples are:**

Discounts Sales Reduction in Population

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**When finding a discount, there are two different methods you can use.**

Find the percent of the original price (discounted amount in $) Subtract the discount from the original price. Method 2: Subtract the percent from 100% (percent you are paying) Find the percent of the original price.

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**Example: A $50 sweater is on sale for 20% off. Calculate the sale price.**

Method 1: Find the percent of the original price (discounted amount in $) Subtract the discount from the original price. Method 2: Subtract the percent from 100% (percent you are paying) Find the percent of the original price. (Discount) (Sale price) (Percent you pay) (Sale price)

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**Using either method, the answer is $17.50**

A manager wants to provide a 30% discount for everything in his store. Find the sale price of a $25 sweater. Using either method, the answer is $17.50 Click to view Method 1 Click to view Method 2 (Percent you pay) (Discount) (Sale price) (Sale price) Click to view answer

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**The pants are on sale for $29.25**

The manager has pants, priced at $45, that he needs to mark down 35%. What will be the sale price of the pants? The pants are on sale for $29.25 Click to view Method 1 Click to view Method 2 (Discount) (Percent you pay) (Sale price) (Sale price) Click to view answer

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**The stereo's original cost is $425. **

Mark wants to purchase a stereo that is on sale, if he is saving at least 30%. The stereo's original cost is $425. What is the most that he is willing to pay for the stereo? Click to view Method 1 Click to view Method 2 (Discount) (Percent you pay) (Sale price) (Sale price) Click to view answer He is willing to pay $ for the stereo.

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**There are situations when the percent of change is going to be an increase. Examples are:**

Tips Sales Tax Increase in Population

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**Tip: An amount added to a bill for services provided**

Tip: An amount added to a bill for services provided. Customers traditionally tip % for good service in restaurants and salons. Example: If the restaurant bill is $45 and you want to leave a 20% tip, how much money should you leave? (45) = or 45(1.20) = 54 The customer will leave $54 on the table. The waitress will receive a $9 tip and the restaurant will receive $45. To calculate the amount of the tip only: .20(45) = 9

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Sales tax: An amount of money that is calculated by applying a percentage rate to the taxable price of a sale. Sales taxes are collected by the buyer from the seller, who turns it over to the government. In NJ the sales tax rate is 7%. To calculate Sales Tax alone find the percent (tax) of the price. That is the amount that you owe in addition to the cost of the item. To find the total cost of an item, you must add the sales tax to the cost. There are 2 ways to do this: Find the percent of the item and add it to the original amount. 2. Find 100% + tax% of the original amount.

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**A car costs $23,500. How much sales tax will the customer pay?**

23,500(0.07) = $1645 What will the customer pay altogether for the car? 23, = $25,145 The total cost of the car, including tax, can be calculated as follows: 23, (23,500) = 25, or 23,500(1.20) = 25,145

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