Section 7.1 Percent, Sales Tax, and Discount. Objective #1: Review converting between fractions, decimals, & percents.

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1 151 Section 7.1 Percent, Sales Tax, an Discount Objective #1: Review converting between fractions, ecimals, & percents. Before we can work problems involving personal finance, we nee to review how to convert between fractions, ecimal, an percents. As an ai, we will be using the TI-30XS calculator. Converting a Fraction to a Decimal: By Han: On TI-30XS: n ) = n or n Type the fraction & hit the key. Then press enter. Write the following to a ecimal: Ex. 1a 5 8 Ex. 1b a) Hit the n key, type 5 on top, arrow own an type 8, an then hit the right arrow. Finally, hit the key an press enter. The answer is b) Type 5 an hit the 2n key an then the n key. Type 31 on top, arrow own an type 200. Press the right arrow key an select the key an press enter. The answer is Converting a Decimal to a Fraction: By Han: Write the number without the ecimal point on top an a 1 followe by the number of zeros equal to the number of igits to the right of the ecimal point on the bottom. Reuce to lowest terms. On TI-30XS: Type the ecimal & hit the key. Then press enter. Write the following to a fraction: Ex. 2a 0.35 Ex. 2b a) Type 0.35, hit an press enter. The answer is b) Type 5.065, hit an press enter. The answer is To write it as a mixe number: 2n key, x10 n key, enter key:

2 152 Converting a Percent to a Fraction: P% = P 100 or P 100 Write the following as a fraction: Ex. 3a 56% Ex. 3b 235.6% Ex. 3c % a) Hit the n key, type 56 on top, arrow own an type 100, an then press enter. Our answer is b) Hit the n key, type on top, arrow own an type 100, an then press enter. If the answer is a ecimal, hit the key an press enter. Finally, to get it as a mixe number, 2n key, x10 n key, enter key: c) Hit the n key, type 13 on top, hit the 2n key an then the n key. Next, enter 1, own arrow an enter 3. Down arrow again an type 100. Press the enter key. The answer is Converting a Fraction to a Percent: F = F 100% Write the following as a percent: Ex. 4a Ex. 4b a) Type 3 an hit the 2n key an then the n key. Type 5 on top, arrow own an type 16. Hit the right arrow, multiply by 100 an then hit enter. Finally, to get it as a mixe number, 2n key, x10 n key, enter key: % b) Hit the n key, type 11 on top, arrow own an type 12. Hit the right arrow, multiply by 100 an then hit enter. Finally, to get it as a mixe number, 2n key, x10 n key, enter key: % 11 12

3 153 Converting a Percent to a Decimal: P% = P 100 This will move the ecimal point two places to the left. We can use money as an analogy for converting percents to ecimals. Since 56 = $0.56, then 56% = The percent is our cent an the ollar is our ecimal. Write the following as ecimals: Ex. 5a 765% Ex. 5b 5.32% a) 765% = = b) 5.32% = = Converting a Decimal to a Percent: D = D 100% This will move the ecimal two places to the right. Again, we can use money as an analogy for converting percents to ecimals. Since $0.56 = 56, then 0.56 = 56%. The ollar is our ecimal an the percent is our cent. Write the following as a percent: Ex. 6a 0.9 Ex a) 0.9 = 0.9(100%) = 90%. b) = 9.548(100%) = 954.8%. Objective #2: Solving problems involving sales tax an iscounts. The key to solve applications with percents is istilling the problem own into a simple sentence. We will start by ientifying the amount, the percent, an the base an filling in the basic sentence: Amount is a Percent of the Base Afterwars, we will set-up the equation using the wor "is" as = an the wor "of" for multiplication. We will then nee to convert the percent into a ecimal or fraction before we can work the problem.

4 We can moify the basic sentence to fit the following applications: 1) Discount: Discount Amount = Discount Rate (as a ecimal) x Original Price 2) Sales Tax: Sales Tax = Tax Rate (as a ecimal) x Item's Price 154 Solve the following: Ex. 7 Juan wants to purchase a new CD player price at $80. If the sales tax is 8.25% of the price, fin the sales tax he will have to pay an fin the total cost for the CD player. Sales Tax = Tax Rate (as a ecimal) x Item's Price We have the Tax Rate (8.25%) an the Item's Price ($80) an we are trying to fin the Sales Tax an then the total cost. Sales Tax = 8.25% x 80 (change 8.25% to a ecimal) Sales Tax = x 80 = $6.60 So, the sale tax is $6.60. The total cost = = $86.60 Ex. 8 If Leroy pai $35 in sales tax on a $400 TV, what was the sales tax rate? Sales Tax = Tax Rate (as a ecimal) x Item's Price We have the Sales Tax ($35) an the Item's Price ($400) an we are trying to fin the Tax Rate. 35 = Tax Rate x 400 (Let R = the tax rate) 35 = 400R (ivie both sies by 400) R = (write as a percent) R = 8.75% The Tax Rate was 8.75%. Ex. 9 A tennis racket that regularly sells for $96 is on sale for 25% off the regular price. Fin the sale price. Discount Amount = Discount Rate (as a ecimal) x Original Price We have the Discount Rate (25%) an the Original Price ($96), we nee to fin the iscount an then fin the sale price. Discount Amount = 25% x 96 (change 25% to a ecimal) Discount Amount = 0.25 x 96 = $24 Sale price = $96 $24 = $72. So, the sale price was $72.

5 155 Ex. 10 A computer system that sol for $1,400 one year ago can now be bought for $980. What is the iscount rate? Discount Amount = Discount Rate (as a ecimal) x Original Price We have the Original Price ($1400), but we o not have the Discount Amount or the Discount Rate. We can fin the Discount Amount by subtracting the new price from the ol price: Discount Amount = = $420 Now, we can fin the iscount rate. 420 = Discount Rate x (1400) (Let R = the iscount rate) 420 = 1400R (ivie both sies by 1400) R = 0.3 (write 0.3 as a percent) R = 30% The Discount Rate was 30%. Objective #3: Applying percent increase an ecrease. In many situations, it is important to fin the percent increase or ecrease of a given quantity. The increase or ecrease is always a percent of the original value. Thus, our basic equation woul look like this: = Percent Change (as a ecimal) x Alternatively, we can use a basic fraction: Solve the following: Ex. 11 A basketball auitorium increase its 19,000 seating capacity by 18%. How many seats were ae to the auitorium? We will want to use our basic equation: Increase = Percent Change (as a ecimal) x We have the Percent Change (18%) an the (19000), so we nee to fin the Increase. Increase = 18% x (19000) (write 18% as a ecimal) Increase = 0.18 x = 3420 Thus, 3420 seats were ae. Ex. 12 A clerk typist was earning $15.50 an hour before the wage was increase to $19.22 per hour. What was percent increase in the wage?

6 We have the ($15.50), but we o not have the Increase or the Percent Change. But, we can fin the Increase by subtracting the ol wage from the new wage. Increase = = $ = 0.24 = 24% So, the wage was increase by 24%. Ex. 13 In settling a claim, the amount of the claim of $1500 was reuce by $500. What was percent ecrease? We have the ($1500) an the ecrease ($500) an we nee to fin the Percent Change = % The amount of the claim was ecrease by %. Objective #4: Abuses of percents. In many areas, incluing avertising, percents can be misuse to eceive someone in how much of a iscount a person may be getting. Usually, the issue arises with mixing what the base is. Solve the following: Ex. 14 In a poll, support for a caniate ecrease from 54% to 45%. A reporter state that support for the caniate roppe by 20%. Is this statement accurate? If not, what is the correct percentage? We have the (54%), but we o not have the Increase or the Percent Change. But, we can fin the Decrease by subtracting the new percent from the ol percent. Decrease = = 9% 9% 54% = 1 6 = % No, the correct percentage is %. 156

7 157 Ex. 15 From a recent avertisement: "Everything has been iscounte 25%. If you come in toay, take an aitional 25% off of the sale price. That is 50% reuction." Is this accurate? To make things easier, suppose an item was originally price at $100. If it ha been iscounte by 25%, then the sale price woul have been: Discount = 25%x100 = 0.25x100 = $25 Sale price = $100 $25 = $75 Now, take 25% off of the sale price: Discount = 25%x75 = 0.25x75 = Final Price = = $56.25 which is not a 50% reuction. The actual Percent Change woul be: = 43.75% 100 No, the statement is not accurate since the actual percent ecrease was 43.75%.