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Ratios and Unit Rates PRE-ALGEBRA LESSON 6-1 Write three fractions equivalent to 4 . 12 Sample answers 1 3 , 2, 6 6 18 6-1 Ratios and Unit Rates PRE-ALGEBRA LESSON 6-1 (For help, go to Lesson 4-4.) Write in simplest form. 1. 30 2. 24 3. 54 4. 12 5. 14 6. 40 35 15 40 60 42 24 Check Skills You’ll Need 6-1 Ratios and Unit Rates PRE-ALGEBRA LESSON 6-1 Solutions 30 30 ÷ 5 1. 35 = 35 ÷ 5 24 6 = 7 54 54 ÷ 6 3. 60 = 60 ÷ 6 3 = 5 12 9 14 14 ÷ 14 12 ÷ 3 4. 15 = 15 ÷ 3 4 = 10 5. 42 = 42 ÷ 14 24 ÷ 8 2. 40 = 40 ÷ 8 = 5 40 40 ÷ 8 6. 24 = 24 ÷ 8 1 5 = 3 =12 3 = 3 6-1 Ratios and Unit Rates PRE-ALGEBRA LESSON 6-1 A survey asked students whether they had afterschool jobs. Write each ratio as a fraction in simplest form. a. all students surveyed to students without jobs all students surveyed students without jobs = 100 Response 60 5 = 3 b. all students surveyed to students with jobs all students surveyed students with jobs After-School Jobs Number Have a Job 40 Don’t Have a Job 60 Total 100 = 100 40 5 = 2 Quick Check 6-1 Ratios and Unit Rates PRE-ALGEBRA LESSON 6-1 The table shows prices for different packages of index cards. Which size has the lowest unit price? Size (cards) Price 100 $2.70 50 $1.30 25 $.75 100 cards: price number of cards $2.70 100 cards = $.027/card 50 cards: price number of cards $1.30 50 cards Find the = $.026/card unit prices. 25 cards: price number of cards $0.75 25 cards = $.03/card The 50-card pack has the lowest unit price. 6-1 Quick Check Ratios and Unit Rates PRE-ALGEBRA LESSON 6-1 Convert 30 gal/min to cups/second. 30 gal 16 c 30 gal/min = 1 min • 1 gal 130 gal = 1 min 816 c • 1 gal 1 min • 60 s • 1 min 260 s Use conversion factors that convert gallons to cups and minutes to seconds. Divide the common factors and units. 1 8c Simplify. = s 30 gal/min equals 8 c/s. Quick Check 6-1 Ratios and Unit Rates PRE-ALGEBRA LESSON 6-1 Write each ratio as a fraction in simplest form. 1. 4 out of 20 students ride the bus to school. 1 5 2. 8 out of 10 students buy lunch. 4 5 Find each unit rate. 3. You pay $4.50 for 2 gallons of orange juice. $2.25/gal 4. You pay $21.60 for a 20-lb bag of dog food. $1.08/lb 5. Convert 15 yd/min to inches/second. 9 in./s 6-1 Proportions PRE-ALGEBRA LESSON 6-2 Evaluate each of the following operations for n = 6. a. Multiply n by 4 and add 6. 30 b. Multiply n by 9 and add 12 66 6-2 Proportions PRE-ALGEBRA LESSON 6-2 (For help, go to Lesson 2-6.) Solve each equation. 1. 4x = 52 2. 3y = 18 3. 5b = 75 4. 7k = 21 Check Skills You’ll Need 6-2 Proportions PRE-ALGEBRA LESSON 6-2 Solutions 1. 4x = 52 4x 4 = 2. 3y = 18 52 4 3y 3 x = 13 3. 5b = 75 5b 5 = = 18 3 y=6 4. 7k = 21 75 5 7k 7 b = 15 = 21 7 k=3 6-2 Proportions PRE-ALGEBRA LESSON 6-2 Solve Method 1 2 y = . 7 14 Multiplication Property of Equality 2 y = 7 14 2 • 14 = y • 14 7 14 28 = y 7 4 =y 6-2 Proportions PRE-ALGEBRA LESSON 6-2 (continued) Method 2 Cross products 2 y = 7 14 2 • 14 = 7 • y 28 = 7y 28 7y = 7 7 4 =y Quick Check 6-2 Proportions PRE-ALGEBRA LESSON 6-2 Do the ratios 3 and 21 form a proportion? Explain. 5 3 5 3 • 35 35 21 35 Test by writing as a proportion. 5 • 21 Write cross products. 105 = 105 Simplify. Yes; the ratios do form a proportion. The cross products are equal. Quick Check 6-2 Proportions PRE-ALGEBRA LESSON 6-2 One hundred rods is about 275 fathoms. About how many fathoms is 25 rods? Let d = distance in fathoms. length in rods length in fathoms 100d = 275(25) d= 275(25) 100 d = 68.75 100 25 = 275 d distance in rods distance in fathoms Write cross products. Divide each side by 100. Simplify. 25 rods is about 68.75 fathoms. Quick Check 6-2 Proportions PRE-ALGEBRA LESSON 6-2 Solve each proportion. 1. a = 5 12 6 10 2. 3 = 6 8 x 16 Does each pair of ratios form a proportion? Explain. 2 0.4 3. 9 = 1.8 Yes; the cross products are equal. 21 14 4. 50 = 25 No; the cross products are not equal. 5. 100 nautical miles equals about 115 statute miles. About how far in ` nautical miles is 50 statute miles? Round to the nearest whole number. about 43 nautical miles 6-2 Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6-3 Find each value of n. a. 18 = n 15 5 n=6 b. 1.5 n = 2.7 4.5 n = 0.9 6-3 Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6-3 (For help, go to Lesson 6-2.) Solve each proportion. Round to the nearest tenth where necessary. 2 f 9 15 1. 3 = 21 3. 4 = p 3 50 16 19 2. 8 = p 4. 3 = g Check Skills You’ll Need 6-3 Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6-3 Solutions 1. 2 f = 3 21 2. 3 50 = 8 p 3. 9 15 = 4 p 4. 16 19 = g 3 3 • f = 2 • 21 8 • 50 = 3 • p 4 • 15 = 9 • p 3 • 19 = 16 • g 3f = 42 400 = 3p 60 = 9p 57 = 16g 3f 42 = 3 3 400 3p = 3 3 60 9p = 9 9 57 16g = 16 16 6.7 = p 3.6 = g f = 14 133.3 = p 6-3 Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6-3 Trapezoid ABCD ~ trapezoid EFGH. Find the value of k. Write a proportion for corresponding sides. Side AB corresponds to side EF. 6 = 3 k 2 Side CD corresponds to side GH. 6 • 2 = k • 3 Write cross products. 6•2 3k = 3 3 4=k Divide each side by 3. Simplify. 6-3 Quick Check Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6-3 A flagpole casts a shadow 5 ft long. At the same time, a yardstick casts a shadow 1.5 ft long. The triangle shown for the flagpole and its shadow is similar to the triangle shown for the yardstick and its shadow. How tall is the flagpole? 1.5 3 = 5 x Corresponding sides of similar triangles are in proportion. 1.5x = 5 • 3 Write cross products. 1.5x 5 • 3 = 1.5 1.5 Divide each side by 1.5. x = 10 Simplify. The flagpole is 10 ft tall. Quick Check 6-3 Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6-3 The scale of a map is 1 in. : 24 mi. About how far is it between two cities that are 3 in. apart on the map? map (in.) actual (mi.) 1 3 = 24 d map (in.) actual (mi.) 1 • d = 24 • 3 d = 72 Write a proportion. Write cross products. Simplify. It is about 72 mi between the two cities. Quick Check 6-3 Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6-3 Solve. 1. Parallelogram ABCD ~ parallelogram EFGH. Find the value of x. 12 2. A girl who is 4 feet tall casts a shadow that is 6 feet long. The tree next to her casts a shadow that is 12 feet long. How tall is the tree? 8 ft 3. The scale on a map is 3 in. : 100 mi. What is the actual distance between two towns that are 9 in. apart on the map? 300 mi 6-3 Probability PRE-ALGEBRA LESSON 6-4 Forty-three boys and five girls tried out for the middle school football team. One-fourth of the students were dropped after the first day. Of those who were left, 1 were dropped after the second day. Of those 6 4 who remained, made the team. How many students made 5 the team? 24 6-4 Probability PRE-ALGEBRA LESSON 6-4 (For help, go to Lesson 5-3.) Simplify. 3. 1 – 17 3 2. 1 – 20 6 11 4. 1 – 12 1. 1 – 8 1 Check Skills You’ll Need 6-4 Probability PRE-ALGEBRA LESSON 6-4 Solutions 1. 1 – 3 2. 1 – 17 8 8 3 8–3 – = 8 8 8 5 = 8 3. 20 20 17 20 – 17 – = 20 20 20 3 = 20 6 11 11 6 11 – 6 – = 11 11 11 5 = 11 4. 1 – 1 1– 12 12 1 12 –1 – = 12 12 12 11 = 12 6-4 Probability PRE-ALGEBRA LESSON 6-4 Find P(rolling a prime number) with one number cube. 3 number of favorable outcomes = 6 number of possible outcomes 3 3 prime-number outcomes (2, 3, 5) 6 possible outcomes 1 P(rolling a prime number) = 6 , or 2 . Quick Check 6-4 Probability PRE-ALGEBRA LESSON 6-4 The probability that a child is an identical twin is 4 in 1,000. Find P(not an identical twin). P(not an identical twin) + P(identical twin) = 1 Write an equation. 4 P(not an identical twin) + 1,000 = 1 P(not an identical twin) + Substitute. 4 – 4 =1 – 4 1,000 1,000 1,000 996 P(not an identical twin) = 1,000 = Subtract 4 from 1,000 each side. Simplify. 249 250 The probability that a child is not an identical twin is 249 . 250 6-4 Quick Check Probability PRE-ALGEBRA LESSON 6-4 You have five different coins in your pocket: a penny, a nickel, a dime, a quarter, and a half-dollar. You pull out one coin at random. What are the odds in favor of the coin being worth less than ten cents? 2 odds in favor = 3 The odds are 2 are worth less than ten cents. 3 are not. 2 , or 2 to 3, in favor of the coin being worth less than ten cents. 3 Quick Check 6-4 Probability PRE-ALGEBRA LESSON 6-4 Find each probability. 1. A letter is selected at random from the letters A, E, I, O, and U. Find the probability that the letter is an A. 1 5 2. In one class, Ms. Lang has 8 boys and 12 girls. She needs to choose one student to help pass out papers. What are the odds that a girl is chosen? 3 2 3. When rolling a number cube, what is P(6)? What is P(not 6)? 1; 5 6 6 6-4 Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6-5 5 Samantha needs a 8 -in. bit for her drill. Should she look in the bin marked 62.5 in., 6.25 in., 0.625 in., or 0.063 in.? 0.625 in. 6-5 Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6-5 (For help, go to Lesson 5-2.) Write each fraction as a decimal. 5 1. 8 4. 5 6 9 2. 20 5. 2 3 3. 3 4 8 6. 11 Check Skills You’ll Need 6-5 Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6-5 Solutions 1. 5 =5÷8 8 2. 9 = 9 ÷ 20 20 = 0.625 = 0.45 4. 6 = 5 ÷ 6 = 0.83 5. 3 = 2 ÷ 3 = 0.6 5 2 6-5 3. 3 =3÷4 4 = 0.75 8 6. 11 = 8 ÷ 11 = 0.72 Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6-5 Write each percent as a fraction or a mixed number. a. 30% 30 100 Write as a fraction with a denominator of 100. 3 10 Simplify. b. 175% 175 100 Write as a fraction with a denominator of 100. 7 4 Simplify. 13 4 Write as a mixed number. Quick Check 6-5 Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6-5 Express 7.3% as a decimal. 7.3% = 7.3 100 = 007.3 Write as a fraction with a denominator of 100. Divide by moving the decimal point two places to the left. You may need to write one or more zeros. = 0.073 Quick Check 6-5 Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6-5 Express 0.412 as a percent. Method 1 0.412 = Rewrite as a fraction. 412 1,000 = 412 ÷ 10 1,000 ÷ 10 = 41.2 100 = 41.2% Method 2 Move the decimal point. 0.412 = 41.2% Quick Check 6-5 Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6-5 Four out of seven members of the chess club are boys. What percent of the chess club members are boys? 4 7 Write a fraction. 0.5714 Divide the numerator by the denominator. 57.14% Write as a percent. About 57% of the chess club members are boys. Quick Check 6-5 Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6-5 Write each percent as a fraction or mixed number, and as a decimal. 1. 325% 13 , or 3 1 ; 3.25 4 4 2. 1.1% 11 ; or 0.011 1,000 Write each as a percent. 3. 2.01 201% 3 4. 5 60% 5. Six out of fifteen students own skateboards. What percent of students own skateboards? 40% 6-5 Proportions and Percents PRE-ALGEBRA LESSON 6-6 A painter uses 3 cans of paint to paint four sets of shelves. How many cans of paint does he need to buy to paint nine sets of shelves? 7 cans 6-6 Proportions and Percents PRE-ALGEBRA LESSON 6-6 (For help, go to Lesson 6-2.) Solve each proportion. 25 x 1. 100 = 28 2. 98.9 43 = x 100 13 52 = x 100 4. 27 x = 150 100 3. Check Skills You’ll Need 6-6 Proportions and Percents PRE-ALGEBRA LESSON 6-6 Solutions 1. 25 x = 100 28 2. 100 • x = 25 • 28 100x = 700 43 • x = 98.9 • 100 43x = 9890 100x 700 100 = 100 43x 9890 43 = 43 x =7 3. 98.9 43 = x 100 x = 230 52 13 = 100 x 4. x 27 = 100 150 13 • 100 = 52 • x 1300 = 52x 100 • 27 = x • 150 2700 = 150x 1300 = 52x 52 52 2700 = 150x 150 150 25 = x 18 = x 6-6 Proportions and Percents PRE-ALGEBRA LESSON 6-6 Find 23% of 158. 23 n = 100 158 Write a proportion. 23(158) = 100n Write cross products. 23(158) 100n = 100 100 Divide each side by 100. 36.34 = n Simplify. 23% of 158 is 36.34. Quick Check 6-6 Proportions and Percents PRE-ALGEBRA LESSON 6-6 What percent of 34 is 28? Round to the nearest tenth of a percent. n 28 = 100 34 Write a proportion. 34n = 100(28) Write cross products. 100(28) 34n = 34 34 Divide each side by 34. n = 82.35... Simplify. 82.4 Round. 28 is approximately 82.4% of 34. 6-6 Quick Check Proportions and Percents PRE-ALGEBRA LESSON 6-6 216 is 72% of what number? 72 216 = 100 n Write a proportion. 72n = 100(216) Write cross products. 72n 100(216) = 72 72 Divide each side by 72. n = 300 Simplify. 216 is 72% of 300. Quick Check 6-6 Proportions and Percents PRE-ALGEBRA LESSON 6-6 A tile floor has 90 blue tiles, which is 15% of all the tiles in the floor. How many tiles are in the floor in all? 90 15 = x 100 Write a proportion. 15x = 100(90) Write cross products. 100(90) 15x = 15 15 Divide each side by 15. x = 600 Simplify. The floor has 600 tiles in all. Check. Is the answer reasonable? The problem says the number of blue tiles is 15%. 10% of 600 is 60, so 5% of 600 is 30, and 15% is 60 + 30 = 90. The answer is reasonable. Quick Check 6-6 Proportions and Percents PRE-ALGEBRA LESSON 6-6 Solve. 1. Find 47% of 2,400. 2. What percent of 700 is 1,498? 1,128 214% 3. 6 is 3% of what number? 200 4. Water covers about 361,736,000 km2, or about 70.8% of Earth’s surface. What is the approximate surface area of Earth? about 511,000,000 km2 6-6 Percents and Equations PRE-ALGEBRA LESSON 6-7 Match each expression in Column 1 with an equivalent expression in Column 2. Column 1 1. 50% of 250 2. 100% of 250 3. 1% of 250 4. 10% of 250 Column 2 a. 250 b. 2.5 c. 25 d. 125 1. d 2. a 3. b 4. c 6-7 Percents and Equations PRE-ALGEBRA LESSON 6-7 (For help, go to Lesson 6-5.) Write each percent as a decimal. 1. 48% 2. 5% 3. 23.8% 4. 72.25% 5. 136% 6. 178.5% Check Skills You’ll Need 6-7 Percents and Equations PRE-ALGEBRA LESSON 6-7 Solutions 48 1. 48% = 100 = 0.48 3. 23.8% = 2. 23.8 100 4. 72.25% = = 0.238 5. 136% = 5 5% = 100 = 0.05 72.25 100 = 0.7225 136 100 6. 178.5% = = 1.36 178.5 100 = 1.785 6-7 Percents and Equations PRE-ALGEBRA LESSON 6-7 What is 35% of 84? n = 0.35 • 84 Write an equation. Write the percent as a decimal. n = 29.4 Simplify. 35% of 84 is 29.4. Quick Check 6-7 Percents and Equations PRE-ALGEBRA LESSON 6-7 What percent of 26 is 65? n • 26 = 65 26n 65 = 26 26 n = 2.5 = 250% Write an equation. Divide each side by 26. Simplify. Change the decimal to a percent. 65 is 250% of 26. Quick Check 6-7 Percents and Equations PRE-ALGEBRA LESSON 6-7 A car salesman makes a 6.5% commission on each car he sells. How much does he make on the sale of a car for $35,000? Words amount of commission is 6.5% of $35,000 • $35,000 Let c = amount of commission. Equation c = 0.065 c = 0.065 • 35,000 = 2,275 The salesman’s commission is $2,275. 6-7 Quick Check Percents and Equations PRE-ALGEBRA LESSON 6-7 During a telephone survey, 414 people, or 46% of those called, said that they were watching station RFGT at the time of the call. How many people were called? Words Equation 414 is 46% of people called Let n = number of people called. 414 = 0.46 • n 0.46n = 414 0.46n 414 = 0.46 0.46 n = 900 Quick Check 900 people were called. 6-7 Percents and Equations PRE-ALGEBRA LESSON 6-7 Solve 1. What is 9% of 30? 2. What is 25% of 312? 2.7 78 3. What percent of 9 is 3? 4. What percent of 3 is 9? 1 300% 33 3 % 5. A car dealer makes an 8% commission on each car she sells. How much does she make on a $40,000 sale? $3,200 6. During a telephone survey, 320 people, or 25% of those called, said they were listening to the same station at the time of the call. How many people were called? 1,280 people 6-7 Percent of Change PRE-ALGEBRA LESSON 6-8 Write these fractions to the nearest tenth of a percent. a. 65 255 25.5% b. 42 52 80.8% 6-8 Percent of Change PRE-ALGEBRA LESSON 6-8 (For help, go to Lesson 6-5.) Write each decimal as a percent. 1. 0.46 2. 2.47 3. 0.03 4. 5.236 Check Skills You’ll Need 6-8 Percent of Change PRE-ALGEBRA LESSON 6-8 Solutions 1. Move the decimal 2 places to the right. 0.46 = 46% 2. 2.47 = 247% 3. 0.03 = 3% 4. 5.236 = 523.6% 6-8 Percent of Change PRE-ALGEBRA LESSON 6-8 Find the percent of increase from 8 to 9.6. amount of increase = 9.6 – 8 = 1.6 percent of increase = amount of increase original amount 1.6 = 8 = 0.2 = 20% The percent of increase from 8 to 9.6 is 20%. Quick Check 6-8 Percent of Change PRE-ALGEBRA LESSON 6-8 In a given year, Hillsboro had a total of 7.5 in. of rain by March 1 and a total of 22.5 in. by July 1. Find the percent of increase from 7.5 to 22.5. amount of increase = 22.5 – 7.5 = 15 percent of increase = amount of increase original amount 15 = 7.5 = 2 = 200% The percent of increase from March 1 to July 1 was 200%. 6-8 Quick Check Percent of Change PRE-ALGEBRA LESSON 6-8 Find the percent of decrease from 1,250 to 1,120. amount of decrease = 1,250 – 1,120 = 130 percent of decrease = = amount of decrease original amount 130 1,250 = 0.104 = 10.4% Quick Check 6-8 Percent of Change PRE-ALGEBRA LESSON 6-8 Solve. 1. Find the percent of increase from 22 to 63. 186.4% 2. Find the percent of decrease from 6.3 to 2.2. 65.1% 3. A surgeon performed 62 operations in 1991. He performed 342 in 2001. Find the percent of increase. 451.6% 6-8 Markup and Discount PRE-ALGEBRA LESSON 6-9 Without computing, explain why 40% of 22 is less than 11. 11 is half, or 50%, of 22, so 40% of 22 is less than 11. 6-9 Markup and Discount PRE-ALGEBRA LESSON 6-9 (For help, go to Lesson 6-7.) Write an equation and solve. Round to hundredths as needed. 1. What is 75% of $82? 2. What is 42% of $170? 3. What is 5.5% of $24? 4. What is 80% of $15.99? Check Skills You’ll Need 6-9 Markup and Discount PRE-ALGEBRA LESSON 6-9 Solutions 1. What is 75% of $82? n = 0.75 • 82 n = 61.5 75% of $82 is $61.50. 2. What is 42% of $170? n = 0.42 • 170 n = 71.4 42% of $170 is $71.40. 3. What is 5.5% of $24? n = 0.055 • 24 n = 1.32 5.5% of $24 is $1.32. 4. What is 80% of $15.99? n = 0.80 • 15.99 n = 12.79 80% of $15.99 is $12.79. 6-9 Markup and Discount PRE-ALGEBRA LESSON 6-9 A grocery store has a 20% markup on a can of soup. The can of soup costs the store $1.25. Find the markup. markup = percent of markup • store’s cost = 0.2 • 1.25 = 0.25 Simplify. The markup is $.25. Quick Check 6-9 Markup and Discount PRE-ALGEBRA LESSON 6-9 A bookstore pays $4.50 for a novel. The percent of markup is 45%. Find the novel’s selling price. 0.45 • 4.50 = 2.03 Multiply to find the markup. 4.50 + 2.03 = 6.53 Store’s cost + markup = selling price. The selling price is $6.53. Quick Check 6-9 Markup and Discount PRE-ALGEBRA LESSON 6-9 A camera that regularly sells for $210 is on sale for 30% off. Find the discount. discount = percent of discount • regular price = 0.30 • 210 = 63 The discount is $63. Quick Check 6-9 Markup and Discount PRE-ALGEBRA LESSON 6-9 Solve. 1. The school store has a 65% markup on each stapler. Each stapler costs the store $2.10. Find the markup. $1.37 2. A clothes store pays $40 for a skirt. The percent of markup is 25%. Find the skirt’s selling price. $50 3. A pair of shoes that regularly sells for $94.99 is on sale for 30% off. What is the sale price? $66.49 6-9 Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6-10 A theater has 25 seats in the first row. Each of the following rows has two more seats than the row before it. How many seats are in the 15-row theater? 585 6-10 Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6-10 (For help, go to Lesson 1-8.) Solve. 1. For two weeks, you double the amount of money you save each day. You save $.01 the first day. How much money will you have at the end of the two weeks? Check Skills You’ll Need 6-10 Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6-10 Solutions Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Amount of new money saved $.01 $.02 $.04 $.08 $.16 $.32 $.64 $1.28 $2.56 $5.12 $10.24 $20.48 $40.96 $81.92 Total amount saved $.01 1 + 2 = $.03 3 + 4 = $.07 7 + 8 = $.15 15 + 16 = $.31 31 + 32 = $.63 63 + 64 = $1.27 1.27 + 1.28 = $2.55 2.55 + 2.56 = $5.11 5.11 + 5.12 = $10.23 10.23 + 10.24 = $20.47 20.47 + 20.48 = $40.95 40.95 + 40.96 = $81.91 81.91 + 81.92 = $163.83 After 2 weeks, $163.83 will have been saved. 6-10 Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6-10 Martin had 100 trees in his orchard the first year. Each year after that he increased the number of trees in his orchard by 10%, rounded to the nearest whole number. How many trees did he have in his orchard in the sixth year? Year 1 2 3 4 5 6 Tree Count at Beginning of Year 100 110 121 133 146 161 Rate of Increase (10%) 0.1 0.1 0.1 0.1 0.1 Martin had 161 trees in the sixth year. 6-10 Increase in Tree Count Tree Count at End of Year 10 11 12 13 15 110 121 133 146 161 Quick Check Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6-10 Solve. 1. For an auction item, the bid starts at $100 and increases 50% every minute. In how many minutes will the bid go over $2,500? 8 minutes 2. Sharon uses her initials, SLF, for her password. How many different three-letter passwords can she make with these letters? 6 passwords 3. In how many ways can you make 45¢ in change using only nickels, dimes, and quarters? 8 ways 6-10