1. Percents

2. A survey asked students whether they had after-school jobs. Write each ratio as a fraction in simplest form. Ratios and Unit Rates a. all students surveyed to students without jobs b. all students surveyed to students with jobs all students surveyed students with jobs 100 40 = = 5252 After-School Jobs ResponseNumber Have a Job40 60 100 Don’t Have a Job Total all students surveyed students without jobs 100 60 = = 5353

3. The table shows prices for different packages of index cards. Which size has the lowest unit price? Ratios and Unit Rates Price $2.70 $1.30 $.75 100 50 25 Size (cards) 100 cards: price number of cards $2.70 100 cards = $.027/card25 cards: price number of cards $0.75 25 cards = $.03/card The 50-card pack has the lowest unit price. 50 cards: price number of cards $1.30 50 cards = $.026/card Find the unit prices.

4. Convert 30 gal/min to cups/second. Ratios and Unit Rates 30 gal/min = 30 gal 1 min 16 c 1 gal 1 min 60 s Use conversion factors that convert gallons to cups and minutes to seconds. 1 min 1 2 60 s Divide the common factors and units. = 1 30 gal 1 min 8 16 c 1 gal = 8 c s Simplify. 30 gal/min equals 8 c/s.

5. Solve =. Proportions 2727 y 14 Method 1:Multiplication Property of Equality = 2727 y 14 14= 14 2727 y 14 = y 28 7 4= y

6. (continued) Proportions Method 2:Cross products = 2727 y 14 2 14= 7 y 28= 7y 4= y = 28 7 7y77y7

7. Do the ratios and form a proportion? Explain. Proportions 105= 105 Simplify. Yes; the ratios do form a proportion. The cross products are equal. 3535 21 35 Test by writing as a proportion. 3535 21 35 3 35 5 21 Write cross products.

8. One hundred rods is about 275 fathoms. About how many fathoms is 25 rods? Proportions Let d = distance in fathoms. length in rods length in fathoms 100 275 = 25 d distance in rods distance in fathoms 100d = 275(25)Write cross products. d = 68.75Simplify. d = Divide each side by 100. 275(25) 100 25 rods is about 68.75 fathoms.

9. Trapezoid ABCD ~ trapezoid EFGH. Find the value of k. Similar Figures and Scale Drawings Write a proportion for corresponding sides. 6k6k Side AB corresponds = Side CD corresponds to side EF.to side GH. 3232 6 2 = k 3Write cross products. = Divide each side by 3. 6 2 3 3k33k3 4 = kSimplify.

10. 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? Similar Figures and Scale Drawings Corresponding sides of similar triangles are in proportion. 1.5 5 = 3x3x 1.5x = 5 3 Write cross products. Divide each side by 1.5. 1.5x 1.5 = 5 3 1.5 x = 10 Simplify. The flagpole is 10 ft tall.

11. 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? Similar Figures and Scale Drawings It is about 72 mi between the two cities. map (in.) actual (mi.) 1 24 3d3d map (in.) actual (mi.) = Write a proportion. 1 d = 24 3Write cross products. d = 72Simplify.

12. Write each percent as a fraction or a mixed number. Fractions, Decimals, and Percents a. 30% b. 175% Write as a fraction with a denominator of 100. 30 100 Simplify. 3 10 Write as a fraction with a denominator of 100. 175 100 1Write as a mixed number. 3434 Simplify. 7474

13. Express 7.3% as a decimal. Fractions, Decimals, and Percents = 0.073 7.3% = Write as a fraction with a denominator of 100. 7.3 100 = 007.3 Divide by moving the decimal point two places to the left. You may need to write one or more zeros.

14. Express 0.412 as a percent. Fractions, Decimals, and Percents Method 1:Rewrite as a fraction. = 41.2% Method 2:Move the decimal point. 0.412 = 41.2% 0.412 = 412 1,000 = 412 ÷ 10 1,000 ÷ 10 = 41.2 100

15. Four out of seven members of the chess club are boys. What percent of the chess club members are boys? Fractions, Decimals, and Percents 0.5714Divide the numerator by the denominator. 57.14% Write as a percent. About 57% of the chess club members are boys. Write a fraction. 4747

16. Find 23% of 158. Proportions and Percents 23(158) = 100nWrite cross products. 36.34 = nSimplify. 23% of 158 is 36.34. = Write a proportion. 23 100 n 158 = Divide each side by 100. 23(158) 100 100n 100

17. What percent of 34 is 28? Round to the nearest tenth of a percent. Proportions and Percents 34n = 100(28)Write cross products. n = 82.35...Simplify. = Write a proportion. n 100 28 34 = Divide each side by 34. 100(28) 34 34n 34 28 is approximately 82.4% of 34. 82.4Round.

18. 216 is 72% of what number? Proportions and Percents 72n = 100(216)Write cross products. n = 300Simplify. = Divide each side by 72. 100(216) 72 72n 72 = Write a proportion. 72 100 216 n 216 is 72% of 300.

19. 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? Proportions and Percents 15x = 100(90)Write cross products. x = 600Simplify. 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. = Write a proportion. 15 100 90 x = Divide each side by 15. 100(90) 15 15x 15

20. What is 35% of 84? Percents and Equations n = 0.35 84 Write an equation. Write the percent as a decimal. n = 29.4Simplify. 35% of 84 is 29.4.

21. What percent of 26 is 65? Percents and Equations n 26 = 65Write an equation. n = 2.5Simplify. = 250% Change the decimal to a percent. 65 is 250% of 26. = Divide each side by 26. 26n 26 65 26

22. 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? Percents and Equations c = 0.065 35,000 = 2,275 The salesman’s commission is $2,275. Words amount of commissionis6.5%of$35,000 Let c = amount of commission. Equationc=0.065$35,000

23. 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? Percents and Equations 0.46n = 414 n = 900 900 people were called. = 0.46n 0.46 414 0.46 Words414 is 46% of people called Let n = number of people called. Equation414=0.46n

24. Find the percent of increase from 8 to 9.6. Percent of Change amount of increase = 9.6 – 8 = 1.6 = 0.2 = 20% The percent of increase from 8 to 9.6 is 20%. percent of increase = amount of increase original amount = 1.6 8

25. 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. Percent of Change amount of increase = 22.5 – 7.5 = 15 = 2 = 200% The percent of increase from March 1 to July 1 was 200%. percent of increase = amount of increase original amount = 15 7.5

26. Find the percent of decrease from 1,250 to 1,120. Percent of Change amount of decrease = 1,250 – 1,120 = 130 = 0.104 = 10.4% percent of decrease = amount of decrease original amount = 130 1,250

27. 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 and Discount markup = percent of markup store’s cost = 0.2 1.25 = 0.25 Simplify. The markup is $.25.

28. A bookstore pays $4.50 for a novel. The percent of markup is 45%. Find the novel’s selling price. Markup and Discount 0.45 4.50 = 2.03Multiply to find the markup. 4.50 + 2.03 = 6.53 Store’s cost + markup = selling price. The selling price is $6.53.

29. A camera that regularly sells for $210 is on sale for 30% off. Find the discount. Markup and Discount discount = percent of discount regular price = 0.30 210 = 63 The discount is $63.