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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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