Transcript Objectives
Page 171 – Percent Problems Objectives Find equivalent fractions, decimals, and percents. Solve problems involving percent. Glossary Terms Percent – a ratio that compares a number with 100 25% of 40 is 10 percent rate – 25 is the percent rate the calculated percentage of the base base (of a percentage) – 40 is the base number of which a percentage is calculated Percentage – 10 is the percentage amount obtained by multiplying a base by a percent rate Meteorology Application Relative humidity is a common example of percent. At 30ºC, 1 cubic meter of air can hold no more than 26 grams of water. At this amount, the relative humidity is 100%. At other amounts, ratios are used to determine the relative humidity. If 1 cubic meter of air at 30ºC contains 6.5 g of water, the relative humidity is 25% because 6.5/26 = ¼ or 25%. Converting between fractions, decimals and percents. Fractions to decimals – divide the numerator by the denominator Decimals to percents – move the decimal point 2 places to the right Fractions to percents – change the fraction to a decimal and the decimal to a percent Percents to decimals – move the decimal point 2 places to the left Decimals to fractions – write the decimal as a fraction and simplify Write each percent as a decimal and as a fraction . 75% = 75 = 0.75 100 75 = 3 100 4 110% = 110 = 1.10 100 1 110 = 11 = 1 10 100 10 4.4% = 4.4 = 44 = 0.044 100 1000 . 44 = 11 250 1000 . . The Equation Method The equation method is a method for finding an unknown part of a percent by setting up an equation 25% of 40 is what number (the percentage is unknown) .25(40) = x 25% of what number is 10 (the base is unknown) .25x = 10 What percent of 40 is 10 (the percent rate is unknown) P · 40 = 10 or 40P = 10 The sophomore class is sponsoring a trip to see a play. Student tickets normally cost $8. If at least 20 people buy tickets, there is a 30% discount. How much will each ticket cost at the discounted price. If there is a 30% discount, that means the discounted price is 70% of the full price, which is $8. So, 70% of $8 is what number? .70(8) = x 5.60 = x So, the discounted price of the tickets is $5.60. Examples What percent of 80 is 15? Find 115% of 200 P · 80 = 15 What is 115% of 200 80P = 15 x = 1.15(200) P = 15 x = 230 80 P = .1875 45 is 40% of what number? 18.75% 45 = .4x 45 = x .4 112.5 = x A VCR with a sale price of $239.40 is advertised as 40% off. What was the original price? Since the price was 40% off, that means the $239.40 is 60% of the original price. So, 239.40 is 60% of what number? 239.40 = .6x 239.40 = x .6 399 = x So the original price was $399. More Applications Many types of problems involve finding a percent of increase or percent of decrease. It’s important to remember in these types of problems that the original amount is always used as the base. Percent of increase or decrease: amount of change = percent of change original amount A family is adding additional rooms to their house. The house originally had 1500 sq ft of floor space. After the additions, the house will have 1800 sq ft. Find the percent of increase. percent of increase = amount of change original amount Amount of change is 1800 – 1500 = 300 original amount is 1500 300 = 0.2 = 20% 1500 . So the percent of increase in floor space is 20%. The price of a car that originally sold for $17,000 has been reduced to $14,450. Find the percent of decrease in the price of the car. amount of change percent of decrease = original amount Amount of change is 17000 – 14450 = 2550 2550 = 0.15 = 15% 17000 . So the percent of decrease was 15%.