1. Approaching problems that deal with percents….. Example: Selina bought a shirt on sale that was 20% less than the original price. The original price was 5 more than the sale price. What was the original price? Explain or show work. 20% Using a “tape diagram” is one way to solve. We can call the original price 100%. Since the sale price is 20% less than the original price, the sale price is actually 80% of the original. The original price is $5.00 MORE than the sale price so it seems logical that this equation would work : Sale price + 5 = original, or 80% + 5 = 100% So…$5.00 must represent 20% of the original. If that is so, then multiply 5 by 5 and you get $25.00 as the original price! SALE PRICE IS 80% $5.00

2. More sample Problems: Selina bought a shirt on sale that was 25% less than the original price. The original price was $12.50 more than the sale price. What was the original price? Show work with a tape diagram. Since $12.50 must represent 25%, multiply $12.50 by 4 and you get the original price. 12.50 x 4 = $50.00 Matthew bought a pair of pants that was 30% off the original price. The original price was $52 more than HALF of the sale price. What was the original price? Show work with a tape diagram. This one can be a little tricky, but if you illustrate properly, you will get the answer! 25% Sale price is 75% of the original $12.50 10% Sale price is 70% of original $10 more than half sale price (half of 70% is 35%) so this is 35% +10 55555555555555555555 This is 35% which is half of 70% This represents $52. So there are 13 parts here. 52 ÷ 13 = 4 So, each 5% is $4.00. There are 20 of these 5% sections in 100% so 20 x 4 = $80 Since 35% is not divisible by 10, you have to break into 5s

3. Student Problems using Tape Diagrams, calculators and equations: 1.Robert had to buy some weights for his bridge because it was holding so much! He bought one package of 20lb weights on sale that was 40% less than the original price. The original price was $76.00 more than the sale price. What was the original price? 2.After figuring out the original price of the package, Robert wanted to make a deal with the store manager and buy some single weights. How much did each single weight cost if there were 8 in a package? 3.Kira needed to buy a new ski suit since she ripped hers on her last ski vacation (which wasn’t too long ago!) She found a ski suit on sale. It was marked down 20% from the original price. The original price was $27.00 more than half of the sale price. What was the sale price AND the original price of the ski suit that Kira bought? 4.The Ski Outfitters Store usually marks up its merchandise by 25%. It bought 48 ski outfits of various sizes for a flat price of $720.00. The store calculated the price of each ski suit and then marked each one up. What would be the price of a single ski suit? How much money is made as profit overall? 5.The Ski Outfitters Store offered a deal. After calculating their markup prices, they advertised buy two outfits and get the third one for 30% discount. What would a customer pay if they bought 3 outfits on a tax free day? 6.Nathan decided to throw a party after his bridge crashing to celebrate the enormous amount of weight his bridge held. He bought a package of cups for $2.50, a package of plates for 15% less than the price of the cups and a package of plastic spoons on sale. The spoons were on sale for 20% less than the original price. The original price of the spoons was $0.36 more than the sale price. Nathan calculated cost before tax. What was that cost? 7.What did Nathan pay at the counter after adding a pack of gum for $0.99 and 7% tax added on?

4. Answers: 1) Robert had to buy some weights for his bridge because it was holding so much! He bought one package of 20lb weights on sale that was 40% less than the original price. The original price was $76.00 more than the sale price. What was the original price? $190.00 If 40% is $76.00, then 20% is $38.00. There are 5 (20%) in 100% so multiply 38 by 5 to get the original price. 38 x 5 = $190.00 2)If one package is $190.00, then divide that by 8 weights in a package. 190 ÷ 8 = $23.75 3)Kira needed to buy a new ski suit since she ripped hers on her last ski vacation (which wasn’t too long ago!) She found a ski suit on sale. It was marked down 20% from the original price. The original price was $27.00 more than half of the sale price. What was the sale price AND the original price of the ski suit that Kira bought? Sale price = $36.00 Original price = $45.00 20% 60% is the sale price40% has to be $76 10% Marked down ski suit = 80% of original 40% is half of 80% Original = 27 + 40% So…..$27 has to represent 60% of original Divide 27 by 6 to find out what each 10% is and you get $4.50 for every 10%. So, $4.50 x 10 will give you 100% which is $45.00

5. Answers Continued: 4)The Ski Outfitters Store usually marks up its merchandise by 25%. It bought 48 ski outfits of various sizes for a flat price of $720.00. The store calculated the price of each ski suit and then marked each one up. What would be the price of a single ski suit? Cost of each ski suit is 720 ÷ 48 = $15.00 + $3.75 = $18.75 25% represents $3.75 markup per outfit and $180.00 profit overall. 5) The Ski Outfitters Store offered a deal. After calculating their markup prices, they advertised buy two outfits and get the third one for 30% discount. What would a customer pay if they bought 3 outfits on a tax free day? 2 ($18.75)= $37.50 $37.50 + $13.13 Total: $50.63 10% 10%Nathan decided to throw a party after his bridge crashing to celebrate the enormous amount of weight his bridge held. He bought a package of cups for $2.50, a package of plates for 15% less than the price of the cups and a package of plastic spoons on sale. The spoons were on sale for 20% less than the original price. The original price of the spoons was $0.36 more than the sale price. Nathan calculost before tax. What was that cost? 10% 25% markup $3.75 /outfit $180/total 10% Sale price for 3 rd outfit is 70% 18.75 x.70 = 13.13 6)$ANSWER: Cups = $2.50 Plates = 85% of $2.50 = $2.13 Spoons: $0.36 represents 20% so original price is $0.36 x 5 = $1.80 Total cost = $2.50 + $2.13 + $1.80 = $6.43 7) $6.43 + $0.99 = $7.42 (0.07 x 7.42 = $0.52tax) So, $7.42 + $0.52 =