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2.7 More about Problem Solving1 Use percent in problems involving rates. Percents are ratios where the second number is always 100. For example, 50% represents the ratio 50 to 100 and 27% represents the ratio 27 to 100. The percent proportion is

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2.7 More about Problem Solving2 1. The parking lot at a grocery has 50 cars in it. 40% of the cars are four- door. How many cars are four-door? Answer: 20 cars 2. Students at East Central High School earned $384 selling subscriptions. They want to make $4350 for a club trip. What percent of their goal has been reached? Round to the nearest tenth of a percent, if necessary. Answer: 8.8% 3. Tech Support spent $53,500 this year on health insurance alone. If total sales were $870,500, what percent of total sales was spent on health insurance? Round to the nearest tenth of a percent, if necessary. Answer: 6.1% 4. An investment broker invests $76,200 in municipal bonds and earns 15% per year on the investment. How much money is earned per year? Answer: $11,430

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2.7 More about Problem Solving3 Solve problems involving mixtures. Use tables to organize the information in the problems. A table enables us to more easily set up an equation, which is usually the most difficult step.

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2.7 More about Problem Solving4 5. A merchant has coffee worth $40 a pound that she wishes to mix with 60 pounds of coffee worth $90 a pound to get a mixture that can be sold for $70 a pound. How many pounds of the $40 coffee should be used? Answer: 40 pounds 6. How many liters of a 10% alcohol solution must be mixed with 90 liters of a 40% solution to get a 20% solution? Answer: 180 L 7. In a chemistry class, 4 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed? Answer: 2 L 8. It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 40 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength? Answer: 10 L

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2.7 More about Problem Solving5 Solve problems involving simple interest. The formula used is I = p r t where I = interest p = principal r = rate t = time

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2.7 More about Problem Solving6 9. Helen Weller invested $10,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on the two investments amounts to 11%? Answer: $5,000 10. Mardi received an inheritance of $70,000. She invested part at 12% and deposited the remainder in tax-free bonds at 10%. Her total annual income from the investments was $7600. Find the amount invested at 12%. Answer: $30,000 11. Walt made an extra $10,000 last year from a part-time job. He invested part of the money at 6% and the rest at 9%. He made a total of $690 in interest. How much was invested at 9%? Answer: $3,000 12. Roberto invested some money at 6%, and then invested $4000 more than twice this amount at 11%. His total annual income from the two investments was $3800. How much was invested at 11%? Answer: $28,000

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2.7 More about Problem Solving7 Solve problems involving denominations of money. (Number of items) (Value of one item) = Total value 30 dimes have a value of (30) (.10) = $3.00 Fifteen $5 bills have a value of (15) (5) = $75

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2.7 More about Problem Solving8 13. A convention manager finds that she has $1370 made up of twenties and fifties. She has a total of 46 bills. How many fifty-dollar bills does the manager have? Answer: 15 bills 14. A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has 5 more of the twenties. The total value of the money is $800. Find the number of five-dollar bills that the teller has. Answer: 28 15. A cashier has a total of 124 bills made up of fives and tens. The total value of the money is $770. How many ten-dollar bills does the cashier have? Answer: 30 16. A woman has $1.70 in dimes and nickels. She has 5 more dimes than nickels. How many nickels does she have? Answer: 8

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2.7 More about Problem Solving9 Solve problems involving distance, rate, and time Let d = distance r = rate t = time Then d = rtr = d / t t = d / r

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2.7 More about Problem Solving10 17. Jay drove 288 kilometers at the average rate of 72 kilometers per hour. How long did the trip take? Answer: 4 hr 18. Jill is 22.5 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 1.5 km/hr. They meet in 5 hours. How fast is Joe walking? Answer: 3 km/hr 19. From a point on a river, two boats are driven in opposite directions, one at 5 miles per hour and the other at 11 miles per hour. In how many hours will they be 64 miles apart? Answer: 4 hr 20. Janet drove 305 kilometers and the trip took 5 hours. How fast was Janet traveling? Answer: 61 km/hr

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Section 2.6 More about Problem Solving. Objectives Solve investment problems Solve uniform motion problems Solve liquid mixture problems Solve dry mixture.

Section 2.6 More about Problem Solving. Objectives Solve investment problems Solve uniform motion problems Solve liquid mixture problems Solve dry mixture.

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