Week 6. FLEW POLISH is an anagram for what 10 letter word?

Successive PercentsWeek 6

FLEW POLISH is an anagram for what 10 letter word?

Opener

Fellowship

Opener

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.

Review Question

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

Some basic info about percentages

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.

Successive Percents

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?

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%

Successive Percents Example

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

Retail Price Sale Price Final Price withCoupon

Overall PercentageChange

Price Amount Saved

$40.00 - $16.00 = $24.00

$24.00 x.20 = $4.80

$24.00 - $4.80 = $19.20

$40.00 x.52 = $20.80

$40.00 - $20.80 = $19.20

$40.00 x .40 = $16.00

Successive Percents Example

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?

Other things you could’ve been asked.

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%.

Example 2

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.

Example 3

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 * x4% decrease overall

Example 4

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

Example 5a

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) = $20X = $20/.56 = $35.71

Example 5b

Percent increase (more than) Percent decrease (less than) Percent of Successive Percents

Review of percents

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

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

Example 1

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%

Example 2

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

Example 3

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

Example 4

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

Example 5

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

Example 6

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

Example 7

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

Example 8

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

Example 9

Activities 8-9 Homework: Part 2 of Final Project