How do you find the original amount and amount of change given the percent change and final amount? For example: At a discount furniture store, Chris offered.

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Presentation transcript:

How do you find the original amount and amount of change given the percent change and final amount? For example: At a discount furniture store, Chris offered a salesperson $600 for a couch. Chris’ offer includes 8% sales tax. If the salesperson accepts the offer, what would be the price of the couch before tax? How much was the tax?

In this lesson you will learn how to find the original amount and amount of change given the percent change and final amount by using proportions and equations.

Let’s Review Solving a Proportion 100x = 25 x x = 900

Solving an Equation 100x = 900 x = 9

A Common Mistake Percent Increase/Decrease = Amount Change 40% increase/decrease in price means you just add/subtract $40 Amount increase/decrease = Final amount Increase/decrease of $40 means the final amount is $40

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

Core Lesson At a discount furniture store, Chris offered a salesperson $600 for a couch. Chris’ offer includes 8% sales tax. If the salesperson accepts the offer, what would the price of the furniture be before tax? How much is the tax?

Change = ? = 8% of Original Original = ? = 100% Final = $600 = 108% of Original Key Information:

$600 is 108% of the unknown original amount 60,000 = 108x $ = x = Original $ = $44.44 = Tax Option 1: Use Proportions

Let Original Amount = x = 100% x plus 8% of x = 108% of x = $600 x x = 1.08x = 600 x = original amount = $ tax = 600 – = $44.44 Adding 8% is the same as 108% of the original amount Option 2: Use Equations

In this lesson you have learned how to find the original amount given the percent of change and final amount by using proportions and equations.

Guided Practice At 5 PM the price of 1 share of stock in Technology Corporation was $24. The price had fallen 20% since 9 AM. What was the price at 9AM? How much did the price decrease?

Extension Activities On average retailers markup their selling prices 250% more than their buying prices. Make a table of the last 10 items your family has purchased. How much did they cost you? How much did they cost the retailer? How much profit did the retailer make?

During the Great Depression the price of stocks fell drastically. Pretend that you owned 500 shares of stock in a company whose price per share fell 90% to a rate of $2.50 per share. What was the price per share before the Great Depression? How much did the value of your stock decrease?

Quick Quiz While watching TV Jen’s blinking rate increased 75% to 30 blinks per minute. What was Jen’s blinking rate before watching TV? How much did it change? This week a computer is 30% off its original price and is selling for $500. What was the original price? How much did it change?