CHAPTER 8 Linear Applications

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80 increased by 20% 0:20 80 16 So, 80 increased by 20% is 80 16 96: 24 increased by 35% 0:35 24 8:4 24 increased by 35% is 24 8:4 32:4 36 increased by 250% 2:50 36 90 36 increased by 250% is 36 90 126 64 decreased by 27% 0:27 64 17:28 64 decreased by 27% is 64 17:28 46:72

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1 46 increased by 60% is _________ 2 78 increased by 125% is _________ 3 16 decreased by 30% is _________ 4 54 increased by 213% is _________ 5 128 decreased by 816% is _________ 6 15 increased by 003% is _________ 7 24 decreased by 1084% is _________

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1 46 increased by 60% is 46 0:60 46 46 27:6 73:6 2 78 increased by 125% is 78 1:25 78 78 97:5 175:5

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CHAPTER 8 Linear Applications

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3 16 decreased by 30% is 16 0:30 16 16 4:8 11:2 4 54 increased by 213% is 54 0:213 54 54 11:502 65:502 5 128 decreased by 816% is 128 0:0816 128 128 10:4448 117:5552 6 15 increased by 003% is 15 0:0003 15 15 0:0045 15:0045 7 24 decreased by 1084% is 24 1:084 24 24 26:016 2:016 Many word problems involving percents t the above model that is, a quantity being increased or decreased Often you can solve these problems using one of the following formats: x : or x : x (for a quantity being decreased by a percent) x (for a quantity being increased by a percent)

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A $100 jacket will be reduced by 15% for a sale What will the sale price be Let x sale price Then, 100 0:15 100 x: 100 15 x 85 x The sale price is $85 More often, the sale price will be known and the original price is not known The sale price for a computer is $1200, which represents a 20% markdown What is the original price Let x represent original price Then the sale price is x 0:20x 0:80x The sale price is also 1200 This gives us the equation 0:80x 1200: 0:80x 1200 1200 x 0:80 x 1500

CHAPTER 8 Linear Applications

The original price is $1500 In the rst example, the percent was multiplied by the number given; and in the second, the percent was multiplied by the unknown You must be very careful in deciding of which quantity you take the percent Suppose the rst problem was worded, An item is marked down 20% for a sale The sale price is $80, what is the original price The equation to solve would be x 0:20x 80x, where x represents the original price A common mistake is to take 20% of $80 and not 20% of the original price The data used in the following examples and practice problems are taken from the 117th edition of Statistical Abstract of the United States Many quantities and percentages are approximate

Examples

The average number of hours of television watched by US adults during 1980 was 1470 By 1995, the number of hours of television viewing increased by about 71% What was the average number of hours of television viewing in 1995 1980 hours 7:1% of 1980 hours 1995 hours 1470 0:071 1470 1470 104:37 1574:37 The average number of hours US adults spent watching television in 1995 was about 1574 On January 1, 1995, the price of a rst class postage stamp was $032, which is a 60% increase from the cost on November 1, 1981 What was the cost of a rst class stamp on November 1, 1981 Let x 1st class price on November 1, 1981 $032 is 60% more than this quantity 0:32 x 0:60x 0:32 1x 0:60x 0:32 x 1 0:60 0:32 1:60x 0:32 x 1:60 0:20 x The price of a rst-class stamp on November 1, 1981 was $020