Unit 6. Day 13.

Today’s Plan 1) Three interesting cases (successive percent change) 2) Review other problems

Example A: A store raises the price on a $100 dress 50% Example A: A store raises the price on a $100 dress 50%. They then put the dress on sale for 50% off. What is the price of the dress? −50% +50% $100 $150 $75

Take an additional 15% off Example B: Two stores have a sale on a $300 camera. Which store has the better deal? Store A: 50% discount Store B: 40% discount Take an additional 15% off 𝑥 𝑥 discount 40 100 𝑥 50 100 discount 15 100 = = = 300 original 300 180 original 50 300 15000 = 100 𝑥 100𝑥 40 300 12000 = 100 𝑥 100𝑥 15 180 2700 100 𝑥 = 100𝑥 100 100 100 100 100 100 150 = 𝑥 120 = 𝑥 27 = 𝑥 $ 3 0 0 $ 3 0 0 $ 1 8 0 − $ 1 5 0 − $ 1 2 0 − $ 2 7 $ 1 5 0 $ 1 8 0 $ 1 5 3

Next day: 5% additional raise Example C: Will Jordan and Frye make the same? Mr. Jordan: $20 per hour 15% raise Mrs. Frye: $20 per hour. 10% raise. Next day: 5% additional raise 𝑥 15 100 raise raise 𝑥 = 10 100 𝑥 5 100 20 original = = original 20 22 15 20 300 = 100 𝑥 100𝑥 10 20 200 100 𝑥 100𝑥 5 22 110 100 𝑥 100𝑥 = = 100 100 100 100 100 100 3 = 𝑥 2 = 𝑥 1.1 = 𝑥 $ 20 $ 20 $ 22 + $ 3 + $ 2 − $ 1.10 $ 2 3 $ 2 2 $ 23.10

Original Amount % Change New Amount Example D: Milk increased from $2.40 per gallon to $3.60 Find the percent increase. $2.40 $3.60 ? Example E: A $3.75 bottle of orange juice is increased by 40%. What is the new price? $3.75 ? 40% Example F: A bottle of water cost $1.75 after a 25% increase. What was the original price? $1.75 25% ?

Example D: Milk increased from $2. 40 per gallon to $3 Example D: Milk increased from $2.40 per gallon to $3.60 Find the percent increase. 2.40 increase 100 𝑥 1.20 increase = original 2.40 original 2.4𝑥 = 120 2.4 2.4 120 2.4 1200 24 𝑥 = = = 50 amount of increase 1.20 0. 5 % increase = = original amount 50%

Example E: A $3. 75 bottle of orange juice is increased by 40% Example E: A $3.75 bottle of orange juice is increased by 40%. What is the new price? 𝑥 increase 40 100 increase = = 140 𝑥 new 3.75 new original original 100 3.75 original original 40 3.75 150 = 100 𝑥 100𝑥 100 100 525 = 100𝑥 1.5 = 𝑥 100 100 5.25 = 𝑥 $ 3 . 7 5 + $ 1 . 5 0 $ 5 . 2 5

Example E: A $3. 75 bottle of orange juice is increased by 40% Example E: A $3.75 bottle of orange juice is increased by 40%. What is the new price? 40% 40 % of $3.75 𝑜𝑓 3.75 0.40 ∙ 3.75 $ 3 . 7 5 − $ 1 . 5 0 3 2 × 3 . 7 5 5 . 2 5 0. 4 1 . 5 1.40 ∙ 3.75 = 5.25

Example F: A bottle of water cost $1. 75 after a 25% increase Example F: A bottle of water cost $1.75 after a 25% increase. What was the original price? increase new 125 25 1.75 1.75 increase new = 100 𝑥 original 100 𝑥 original 5 4 = 1.75 𝑥 5𝑥 = 7 5 5 𝑥 = 1.4

Example F: A bottle of water cost $1. 75 after a 25% increase Example F: A bottle of water cost $1.75 after a 25% increase. What was the original price? 𝑥 ∙ 1.25 = 1.75 1.25𝑥 = 1.75 1.25 1.25 1 7 5 1 2 5 . 𝑥 = . 5∙5∙7 = 5∙5∙5 = 1.40