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Activity 4 Problem 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 .7) $212.5 What a lot of you did: Notice, though, x *(1 .7) $125 $212.5*(1 .7) $63.75 x *(1 .7) $125 Same as: $125 x .7 x Multiply both sides by x: Add x to both sides: Factor out an x: $125 x *(.3) $125 x .7 x $125 x .7 x $125 x *(1 .7) x $125 $416.67 x .3 Let’s say you have $100 and you increase this by 5% to get to… $100*(1+.05) = $105 If you decrease $105 by 5% you get: $105*(1-.05) =$99.75 What is the overall percentage change? Started with $100 Ended with $99.75 $99.75 $100 $100 .0025 or .25% Dog 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 are the overall percentage savings? The sale price: $40*(1-.4) = $24 Determine the final price with coupon: $24*(1-.2) = $19.20 The overall percentage change?? New Value - Reference Value Reference Value ($19.20 $40) .52 or 52% $40 Not 60% 45.00 40.00 $40.00 x .40 = $16.00 35.00 $40.00 x.52 = $20.80 30.00 25.00 $24.00 x.20 = $4.80 20.00 $40.00 - $16.00 = $24.00 15.00 $24.00 - $4.80 = $19.20 10.00 $40.00 - $20.80 = $19.20 5.00 0.00 Retail Price Sale Price Price Final Price with Coupon Amount Saved Overall Percentage Change KSDK.com Currently, the individual income tax is 5 percent and the corporate tax is 7 percent. Kay's legislation would roll back Illinois' income tax to 3 percent and the corporate tax to 4.8 percent. Gov. Pat Quinn signed the legislation that temporarily increases the Illinois income tax rate by two-thirds. The move was meant to help close a $15 billion budget deficit that threatens to cripple state government. The full increase is supposed to last just four years. After that, the rates will fall but not all the way back to their original level. If the Illinois state income tax last year (2010) was .03 and it increased to .05 this year (2011), by what percentage did it increase? .05 .03 .667 or 66.7% .03 If the Illinois state income tax in 2011 is .05 and then in 2015 it’s rolled back to .035 what is the percentage decrease from 2011 to 2015? .035 .05 .3 or 30% decrease .05 What is the overall percentage increase over the five years from 2010 (.03) to 2015 (.035)? .035 .03 .1667 or 16.67% .03 Note that the answer is not 66.67 – 30 = 36.67% • The absolute quantity is a measure of the absolute occurrence of the variable. • The relative quantity is the absolute quantity divided by some other quantity. • Three kinds of relative quantities… Percentages Fractions or percents are used when comparing part to total of the same type of variable. (example: percent of adults with HIV) Sorting Autosum Change to percent / decimal Rates Rates are used to compare different types of variables (example: tickets per person, miles per hour, or crimes per 1000 people) Map it Ratios Ratios are used to compare the same type of variable from two sources. California’s population is 33,872,000 and Oregon’s population is 3,421,000. Clearly CA’s population is larger but how many times larger? 33,872,000/3,421,000 = 9.90 Absolute or Relative? I have 16 cheeseburgers. I have 100% more cheeseburgers than you. I have 2 times as many cheeseburgers as you. You have 8 cheeseburgers. I eat 3 cheeseburgers per hour. Absolute or Relative? I have 16 cheeseburgers. Absolute I have 100% more cheeseburgers than you. Relative I have 2 times as many cheeseburgers as you. Relative You have 8 cheeseburgers. Absolute I eat 3 cheeseburgers per hour. Relative