Chapter 6 Percents

Warm-up Write 20% as a decimal and as a fraction in simplest terms. Find 64% of 75 3. Solve each proportion using cross products: n/32 = ¼ 42/n=3/4 1. 0.2 & 1/5 2. 48 3. n=8, N=56

6.5 Solving Percent Problems Using Proportions In a Market, 44 of the 80 types of vegetables are grown locally. What percent of the vegetables are grown locally? Use a model to help find this percent Write a proportion and find the percent: 44/80 = n/100 n= 55

Real World Problem Solving Problem: Music: In a school band of 24 students, 9 students play brass instruments. What percent of the band members play brass instruments? Use a model to help find this percent Write a proportion and find the percent: 9/24 = n/100 n= 37.5

Finding the Whole Using Proportions Problem: 54 is 20% of what number? Use a model to help find this percent Write a proportion and find the percent: 54/n = 20/100 n= 270

Real-World Problem Solving Budgeting: Suppose you have a part-time summer job. You decide that 30% of your earnings can be spent on entertainment. You plan a movie and pizza night with friends that will cost you $10.50. How much will you need to earn at your job in order to stay within your budget? Use a model to help find this percent Write a proportion and find the percent: 10.50/n=30/100 n= $35

6.5 Warm-up (Review) Use a model and write a proportion to solve these problems. 24 is what percent of 32? 2. A school holds classes from 8 am to 2 pm. For what percent of a 24-hr day does this school hold classes? 3. 21 is 84% of what number? 1. 75% 2. 25% 3. 25

6.6 Solving Percent Problems Using Equations Finding the Part: What number is 39% of 377? Write equation with words: “a number” is 39% of 377 Fill in with numbers: n=0.39 * 377 Solve: n=147.03

Finding the Whole Skiing: In New Hampshire, a ski resort is able to open 60% of its runs to skiers. There are 27 runs open. How many runs are there at this resort? Write Equation with words: 60% of (# of skiers) = 27 Write equation with numbers: 0.60 * x = 27 Solve: X = 45

Finding the % Recreation: Of 3,072 teens surveyed, 2,212 say they read for fun. What percent of the teens say they read for fun? Write the equation with words: a percent of 3,072 is 2,212 Write algebraic equation: p * 3,072 = 2,212 Solve: p= 72%

6.6 Warm-up (Review) 18% of 90 is what number? What number is 5% of 522? A person is on a 1,500-Calorie eating plan of which 24% of the Calories are from protein. How many Calories are from protein? Answers: 1. 16.2 2. 26.1 3. 360 Calories

6.7: Applications of Percent Finding Tax and Tips Sales Tax=tax rate * purchase price Ex: A desk you plan to buy costs $159.99. In the state where you are shopping, the sales tax rate is 6%. What will you pay for the desk? 0.06 * 159.99 = 9.60 (tax) 159.99+9.60 = $169.59 (add Tax to cost of item)

Tips A tip is a percent of a bill that you give the person providing a service (15% seems reasonable) Using Mental Math: Step 1: Round the bill to the nearest dollar Step 2: Find 10% by moving decimal 1 place to the left. Step 3: Find 5% by taking ½ of step 2 Step 4: Add the amounts of step 2 and step 3 to find 15%

Estimating a tip (Practice) Ex: Consumer. Your family takes a taxi to the train. The taxi fare is $17.85. Find the amount of a 15% tip for the taxi driver. 17.85 roughly equals 18 0.1 * 18 = 1.8 ½ * 1.8 = 0.9 1.8 + 0.9 = 2.7 $2.70

Real World Problem Solving Restaurants: Suppose you treat a friend to lunch. The total cost of the food items is $9.68. A 7% sales tax will be added and you want to give a tip of 20% for excellent service. How much will you pay for lunch? Find the sales tax: 0.07 * 9.68 = 0.68 Find the tip: 9.68 roughly equals 10 0.2 * 10 = 2 Total = food bill + tax + tip =9.68 + .68 + 2 = $12.36

Finding Commissions Commission = commission rate * sales Ex: Find the commission on a $500 Sale, with a commission rate of 12.5%. 0.125 * 500 62.5

Real World Problem Solving Earnings: A salesperson receives a salary of $650 each week, plus a commission of 4% of all sales. In one week, his sales are $1,250. What does the salesperson earn that week? Total earnings = salary + commission T = 650 + (0.04 * 1,250) = 650 + 50 =700

6.7 Review (Warm-up) The price of a coat is $114 before sales tax. The sales tax is 7% Find the total cost of the coat. Estimate a 15% tip for $30.80. 3. How much money do you get to take home if your salary is $200 and you make 10.5% commission on a sale of $3,000. 1. $121.98 2. $4.65 3. $515

6-8: Finding Percent of Change Percent of change—the percent a quantity increases or decreases from its original amount. Step 1: subtract to find the amount of change. Step 2: Use the proportion: Amount of change / original amount = percent of change / 100

Finding a Percent of Increase North Carolina had 12 seats in the US house of representatives in the 1990s. After the 2000 census, North Carolina had 13 seats. Find the percent of increase in the number of representatives. 13-12=1 1/12=n/100 12n=1(100) N=8.333333 or 8.3%

Markup—the difference between the selling price and the original cost (store’s cost) Finding the Percent Markup: Markup= selling price – original cost Amount of markup/ original cost = percent of markup / 100 Q: An electronics store orders sets of walkie-talkies for $14.85 each. The store sells each set for $19.90. What is the percent of markup? 19.90-14.85=5.05 (markup) 5.05/14.85=n/100 n=roughly 34%

Finding a Percent of Decrease Discount—the difference between the original price and the sale price of an item Q: During a clearance sale, a keyboard that normally sells for $49.99 is discounted to $34.99. What is the percent of discount? 49.99-34.99=15 (discount) 15/49.99=n/100 n roughly equals 30%

6-8 Review (Warmup) 1. Find the percent of increase: 60 to 75. 2. Find the percent of discount (round to the nearest tenth of a percent) Original price $70; sale price $63 3. Find the percent of markup. Round to the nearest tenth of a percent) Original cost $22; selling price %33 1. 25% 2. 10% 3. 50%

6.9: Write an Equation Clothing: A coat was originally $140, but then it was discounted 60%. At the register, a second discount was given for an unknown percent. The receipt says the final price is $33.60. What was the second discount? *Read and understand *Plan and solve Multi-step Problem: 140 * .4 = $56 after the first discount $56-$33.60=$22.40 the amount of the second discount D * 56 = 22.40 (write an equation to solve for D=second discount) Solve: D=40%

Practice: Jewelry: A jewelry store buys a pair of diamond earrings for $90 and sells the pair for $315. What is the maximum percent of discount the store can give and still make $60 profit. *Read and understand *Plan and solve $90 + $60 = $150 (discount will be $315-150=$165) d * 315 = 165 (write equation to find max % of discount) d=52% (solve for d, the Max % of discount the store can offer)

Review 6-9 (Warmup) During a 25% off sale, a furniture store sells a couch for $450. Another store sells the same couch for $750. Find the percent of discount for the original price of the couch compared to the price of the couch at the second store. Answer: 20%