Investigation 3: Markups, Markdowns, and Measures: Using Ratios, Percents, and Proportions

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1 Comparing and Scaling: Ratios, Rates, Percents & Proportions Name: Per: Date Day 1 Fri, Feb 1 Day 2 Mon, Feb 4 Day 3 Tue, Feb 5 Day 4 Wed, Feb 6 Day 5 Thur, Feb 7 Day 6 Fri, Feb 8 Investigation 3: Markups, Markdowns, and Measures: Using Ratios, Percents, and Proportions Standards Learning Target/s I can use proportional relationships to solve multistep percentage problems. I can use proportional relationships to solve multistep percentage problems. I can use proportional relationships to solve conversion problems. I can review for the unit test and make a study plan for myself based on my strengths/challenge areas. Classwork (Check Off Completed/ Corrected Items) Day 1 Pg. 2-3: Inv 3.1 Proportions with percent Day 2 Pg. 5-6: Inv. 3.1, Proportions with percent Exit Ticket Day 3 Pg. 8-9: Inv. 3.2 Begin Unit Review Correct Unit Review Homework (Check Off Completed/ Corrected Items) Pg. 4: CS 3.1 Day 1 Correct with EDpuzzle Pg. 7: CS 3.2-Day 2 Take notes with EDpuzzle Complete Inv. 3 Packet (All Pages) Packet Signature Complete and correct unit Review Study for test Self-Assess Your Understanding of the Learning Target/s I can show understanding of unit standards. Comparing and Scaling Unit Test Enjoy your weekend! 7.RP.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.RP.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane (observing whether the graph is a straight line through the origin). 7.RP.2c: Represent proportional relationships by equations. 7.RP.2d: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Important Dates: CS Inv 3 Packet Due Friday, Feb 8 I have reviewed with a parent/guardian and I am satisfied with the work produced in this packet. Student signature: Parent/Guardian Signature: Date: Date: 1

2 CS Inv. 3 Day 1 - CS 3.1 part 1: Commissions, Markups, and Discounts Proportions with Percents Determine Whether Two Quantities are in a Proportional Relationship (7.RP.2a) 1. Circle ALL the equations below that show a proportional relationship between x and y. A. y = 6x B. y = x 6 C. y = 3x + 2 D. y = x 2 2. Circle ALL the tables below that represent a proportional relationship between x and y. 3. Circle ALL the graphs below that show a proportional relationship between x and y. A. B. C. D. Summary: How can you tell if an equation, table, or graph is a proportional relationship? Equation Table Graph 2

3 Salespeople who sell cars, houses, and fancy jewelry often work on commission. Typically, a commission is a of the sale price of an item. Alternatively, a commission may be a percentage of the item s markup. The markup is the between the buying price, the cost for a store or dealer to buy an item, and the selling price, the price the store or dealer sets for their customers. To make a profit, the selling price must be higher than the buying price. Huan sells cars at Carla s Used Cars. A. At Carla s Used Cars, Huan earns a commission that is 25% of the markup on the car. Huan recently sold a sedan ($300 markup), SUV ($500 markup), and convertible ($950 markup). Car Markup Commission Buying Price Selling Price Sedan $300 SUV $500 Convertible $ For each car, what was Huan s commission in dollars? Add each value to the table above and then explain how you found the commissions. 2. At Carla s, the markup on a car is 10% of the buying price, the price at which Carla bought the car. a. For each car, what was the buying price? Add each value to the table above and then explain how you found the buying prices. b. For each car, what was the selling price? Add each value to the table above and then explain how you found the selling prices. 3

4 HOMEWORK CS Inv 3 Day 1: Complete and then correct with EDpuzzle A. Recently Huan received a job offer from Otto s Used Autos. At Otto s, the markup is 15% of the buying price. The commission at Otto s is 20% of the markup. Huan wonders whether he will get higher commissions at Carla s or at Otto s. 1. Otto also bought a minivan for $20,500. What would be the markup on the minivan? 2. What would be the commission on the minivan? 3. Should Huan work for Carla or for Otto? Explain. (Hint: Look at yesterday s class work to find the commission he would make on the minivan if he worked for Carla.) A. Identify which estimate seems to the most reasonable: 1. 5% tax on a $42 purchase: Under $2 Exactly $2 Over $2 2. 9% tax on a $59.99 purchase: Under $6 Exactly $6 Over $6 B. Find the sales tax for each item. Set up and solve proportions. 1. A sweater for $36 at 7% sales tax = 2. A skateboard for $62.80 at 6% sales tax = 4

5 CS Inv 3 Day 2 - Inv. 3.1 part 2: Commissions, Markups, and Discounts Proportions with Percents A. Set up proportions to answer the following questions. i. Jackson uses 1 cup of cranberry juice for every 1 cup of raspberry juice to make a fruit drink. How many cups of 8 4 cranberry juice will he need to use for 1 1 cups of raspberry juice? Express your answer as a proportion. 2 ii. If a person walks ½ mile in each ¼ hour, How far will they go in 1 hour? iii. Ms. Pullins has a 16-ounce mug filled with hot chocolate. She drinks 9 ounces. What is the percentage of ounces that she has left in her mug? Round your answer to the nearest tenth. Express your answer as a proportion. iv. Mrs. Shi rides her unicycle on a regular basis wearing a clown suit for funsies. She can travels ¾ of a mile in 1/3 of an hour. How long will it take Mrs. Shi to travel 9 miles. v. Mrs. Cullen has a 20 ounce energy drink. She drinks 12 ounces. What is the percentage of ounces that she has left in her mug? Round your answer to the nearest tenth. Express your answer as a proportion. 5

6 A. Bill s Bikes sells new and used bikes. Bill buys used bikes, fixes them, and marks up the prices by 80%. The salesperson selling the bike gets a 25% commission on the markup. 1. Find the missing values in the table. Costs and Revenue for Roberto s Sales Buying Price Markup (80% of buying price) Selling Price Commission (25% of markup) Profit (money the shop makes on the sale) $100 $80 $180 $20 $60 $10 $55 $125 6

7 HOMEWORK CS Inv 3 Day 2: Complete and then correct with EDpuzzle You can use unit rates, such as 3 feet per yard, to convert measurements. The following relationships may be helpful in our next class work problems. You can also use proportions to convert measurements. For example: = A. Kate walks 5 miles in 2 hours at a steady pace. How far can she walk in 1 hour and 15 minutes? Strategy: Set up and solve a proportion with a scale factor: = 1 hour and 15 minutes = hours B. There are 276 calories in 6 ounces of chicken. How many calories are in 1 pound of chicken? Strategy: Find a unit rate and scale up with a scale factor: = = 1 pound = ounces C. One cup of whole milk has 8 grams of fat. How many grams of fat are in a gallon of whole milk? Strategy: Use a rate table, find a unit rate, and scale up with a scale factor: 1 gallon = cups Grams of Fat Cups of Milk D. Choose your own strategy and solve the problem below: Nathan s lawnmowers use 2/3 of a tank of gas to cut three one-acre lawns, How many one-acre lawns can he cut with a full tank of gas? 7

8 CS Inv 3 Day 3 - Inv. 3.2: Measuring to the Unit Measurement Conversions Choose a strategy to solve each problem ratios, proportions, unit rates, rate tables, equations, etc.: A. Chetan makes a necklace for his sister. Twelve beads take up 5 inches of strong. How many beads fit on 1 foot of string? B. Chetan wants to make a necklace with 50 beads. He knows that 12 beads take up 5 inches of string, but the store only sells string by the centimeter. How many centimeters should he buy? (Note: 1 inch = 2.5 centimeters) C. Sean walks ¾ of a mile in 15 minutes. At the same pace, how far can Sean walk in 1 hour and 20 minutes? D. Maren walks 3/5 mile in 24 minutes at a steady pace. How long does it take her to walk 2 miles? (Give your answer in minutes.) E. Half an avocado has about 160 calories. How many calories do a dozen avocados have? F. There are about 1.5 grams of fat in 1 tablespoon of hummus. How many grams of fat are in 2.5 cups of hummus? (Note: 16 tablespoons = 1 cup) 8

9 G. Claire and Pam consider the two situations below. Marking up the price 25% and getting 10% commission on the mark-up Marking up the price 10% and getting a 25% commission on the mark-up Will these situations result in the same commission, or will one commission be greater? Mathematical prove your thinking (Hint: pick a price to calculate for both scenario). E. Ms. Pullins, Mrs. Shi and Mrs. Cullen ae poor teachers. They each work a second job of selling cars in the evening. Ms. Pullins sells cards for Mazda, Mrs. Cullen works for Porsche, and Mrs. Shi works for Lincoln. Complete the table. Whole-sale cost Mark up (75%) Total Selling price Commission (15% of mark-up) Ms. Pullins Profit (Money the shop makes on the sale) $15,000 Mrs. Cullen $53,000 Mrs. Shi $24,000 9

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