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Successive Percents

Successive Percents. Week 6. Opener. FLEW POLISH is an anagram for what 10 letter word? . Opener. Fellowship. Review Question. A town has grown rapidly in the last ten years and has become three hundred percent of what it was before. Equivalent statements:

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Successive Percents

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  1. Successive Percents Week 6

  2. Opener FLEW POLISH is an anagram for what 10 letter word?

  3. Opener Fellowship

  4. Review Question A town has grown rapidly in the last ten years and has become three hundred percent of what it was before. Equivalent statements: The town has experienced _______ percent increase in population. The population now is _____ times as big.

  5. Some basic info about percentages If you want to find a certain percentage of a number, multiply the number the percent (decimal version). E.g. 80% of 300 is .8 * 300

  6. Successive Percents • More than one percent change. • Need to calculate the overall percentage change • between the Final Value and the Beginning Value • You CANNOT just add up the two percent changes.

  7. Successive Percents Example • Jeans are on sale for 40% off the retail price. The retail price is $40.00. If you have a coupon, you can receive an additional 20% off the sale price. What is the overall percentage savings?

  8. Successive Percents Example • What is the overall percentage savings? • Not 60% • You’re paying 0.6 * 0.8 = .48 = 48% of the original cost. • Therefore, overall percentage savings is 100-48 = 52%

  9. Successive Percents Example

  10. Other things you could’ve been asked. • You were asked: What is the overall percentage savings? • Alternate 1: What is the final cost? • Alternate 2: What percent of the original cost are you paying? • Alternate 3: How much did you save?

  11. Example 2 • A politician promises, “If elected, I will cut your taxes by 20% for each of the first three years of my term, for a total of 60%.” Evaluate the promise. • After 3 years, you’re paying x * 0.8 * 0.8 * 0.8 = .512 * x= 51.2% of what you were paying • So he’s actually cutting 48.8% of your taxes and not 60%.

  12. Example 3 • Spot prices for crude oil are rather volatile.  From 1998 to 1999, spot prices for crude oil decreased by 28%.  From 1999 to 2000, they increased by 106%.  What was the percentage change over the two year period from 1998 to 2000? • End of 2000, you’re paying (1-.28)*(1+1.06) = 1.48 = 148% • This means 48% increase.

  13. Example 4 • Your portfolio suffered a 20% loss last year. This year, your portfolio performed well and increased by 20%. What is the overall percentage gain or loss? (Notice we’re never told how much we started with.) x * 0.8 * 1.2 = .96 * x 4% decrease overall

  14. Example 5a • Suppose JC Penny is offering a 30% sale on all their shoes. Some of these shoes are on clearance and you can take off 20% off the sale price. If you find a pair you like that’s on clearance that originally costs $60, what is the final price? $60 * (.7) * (.8) = $33.6

  15. Example 5b • If you find another pair that you like that is also on clearance that you pay $20 for in the end, how much was the pair originally? X * (.7) * (.8) = $20 X = $20/.56 = $35.71

  16. Review of percents • Percent increase (more than) • Percent decrease (less than) • Percent of • Successive Percents

  17. First identify what kind of percent problem it is. Know what you’re looking for!

  18. Example 1 • A town has 999 residents in the year 2000. In 2005, the size of the town is 1023. By what percentage did the population of the town increase? • (1023-999)/999= .024 = 2.4% increase

  19. Example 2 • A town has 999 residents in the year 2000. In 2005, the size of the town is 1023. What percentage of the population in 2005 is the population in 2000? • 999/1023= 0.9765 = 97.7%

  20. Example 3 • A town has 999 residents in the year 2000. In 2005, the size of the town is 768. By what percentage did the population of the town decrease? • (768-999)/999=-.2312=23.12% decrease

  21. Example 4 • A town has 999 residents in the year 2000 and increases by 13% in five years. What is the population of the town in 2005? • 999*(1+.13)= 1128.87 = 1129 people

  22. Example 5 • A town has a population of 1050 in the year 2005. This represents a 26% increase since 1980. What was the population in 1980? • 1050=(1+.26)*x • x = 1050/1.26 = 833 people

  23. Example 6 • In 1996, 94,007 tons of waste was recycled in Chicago’s blue bag recycling program. In the year 2000, 296,363 tons were recycled. By how many percent did it increase from 1996 to 2000? • (296363-94007)/94007 = 2.15 = 215% increase

  24. Example 7 • Chlorofluorocarbons (CFC’s) are chemicals used in air conditioners and refrigerators. They are known to damage the earth’s protective ozone layer. In 1971, the US produced 341,600 metric tons of CFC’s. By 1992, production had decreased to 216,200 metric tons. By what percent did CFC production decrease? • (216200-341600)/341600 = -.367 = 36.7% decrease

  25. Example 8 • Consumer debt has soared 39% in the last five years and is now $1.3 trillion. What was consumer debt five years ago? • X * (1 + 0.39) = 1.3 • X = 1.3/1.39 = $.935 trillion = $935 billion

  26. Example 9 • In 1994, Zaire’s per capita GNP was $125 (70% lower than it was in 1958). What was Zaire’s per capita GNP in 1958? • 125 = (1 - 0.7) * x • x = 125 / 0.3 = $416.67

  27. Activities 8-9 • Homework: Part 2 of Final Project

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