1. More Percentages LSP 120 Joanna Deszcz Week 6

2. Successive Percentages Overall percentage change between ▫Final Value and ▫Beginning Value when you are given two or more intermediate ▫percentage decreases ▫percentage increases ▫or a mixture

3. Example 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?

4. Visually…

5. The Math… Determine the sale price: ▫40 – (40 *.40) = 24 or 40*(1-.4) =24 Determine the final price with coupon: ▫24 – (24 *.20) = 19.20 or 24*(1-.2)=19.20 Determine the overall percentage change: ▫(19.20-40)/40 which is an overall savings of 52%.

6. Try this one… 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.

7. One More… 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?

8. Reworking Percentage Change Original Formula ▫(New-Old)/Old = % Reworked Formulas ▫Old + % * Old = New or Old*(1+%)=New ▫Old = New 1 + %

9. Reverse Percentage Change Formulas Used when the new value and percentage are known – like a price value Need to find the old (Original price) value Use N= P * (1 + r) or N= P * (1 - r) but the original value (P) is unknown.

10. Example Shoes at the local department store are discounted 30%. You buy a new pair of shoes and the sale price is $55.30. What was the original price of the shoes? 55.30 = P * (1 -.30) 55.30 =.70P 55.30/.70 = P 79 = P Original Price of shoes is $79

11. More Examples… Percentage Worksheet