Section 2.6 Percent, Rate, and Mixture Problems 163 21. What is the percentage increase in the time it takes to complete a bachelor’s degree for students attending one public 4-yr college and students attending three or more institutions? Round to the nearest hundredth of a percent. 22. What is the percentage increase in the time it takes to complete a bachelor’s degree for students attending only one private institution and students beginning at public 2-yr colleges? Round to the nearest hundredth of a percent. 23. New York City is the most populated city in the United States. The 2000 census reported that NYC had a population of 8,008,278. In 2009, the population was estimated to be 8,391,881. By what percent did the population increase from 2000 to 2009? Round to the nearest hundredth of a percent. (Source: www.census.gov) 24. China is the world’s most h t t did th populated country. In 2004, the population of China was 1,288,307,000. In 2010, the population was estimated to be 1,330,141,295. By what percent did the population increase from 2004 to 2010? Round to the nearest hundredth of a percent. (Source: http://internetworldstats.com) For each simple interest problem: (1) use a chart to organize the information, (2) write an appropriate equation, (3) solve the equation, and (4) write the answer in complete sentences. (See Objective 2.) 25. Rob earns a $20,000 bonus for the year. He invests this money in two accounts. One account is highly risky but earns 11% annual interest. The other account is less risky and earns 5% annual interest. If Rob earns a total of $1300 in interest for the year, how much did he invest in each account? 26. Marissa has saved $4000 over the last several years. She invests part of her money in a CD that earns 6% annual interest and the rest in a savings account that pays 4% annual interest. If Marissa earns $210 in interest for the year, how much did she invest in each account? 27. Isaiah invests some money into a money market account that earns 10% annual interest. He also invests $3000 less than the amount invested in the money market account in a CD that earns 5.5% annual interest. If he earns $1385 in interest for the year, how much did he invest in each account? 28. Georgia receives an inheritance of $100,000. She invests this money in two different accounts. She invests part of the money in the stock market and earns an average of 12% annual interest. She invests the rest of the money in a money market account that earns 7% annual interest. If Georgia earns $11,000 in interest for the year, how much did she invest in each account? For each mixture problem: (1) use a chart to organize the information, (2) write an appropriate equation, (3) solve the equation, and (4) write the answer in complete sentences. (See Objective 3.) 29. Thomas has a collection of nickels and quarters. He has three times as many quarters as nickels. If the collection is worth $24, how many nickels and quarters does he have? 30. Samantha has a total of 300 coins, which consist of dimes and quarters. If her collection is worth $46.50, how many of each coin does she have? 31. A bank teller has a collection of $10 bills and $20 bills. He has fifteen more $20 bills than $10 bills. The value of his collection is $900. How many of each bill does he have? 32. A department store clerk has only $5 bills and $10 bills in her cash register. She has a total of 30 bills and the value of the collection is $215. How many of each bill does she have? 33. A lab technician needs a 40% alcohol solution. He has 10 gal of a 35% alcohol solution. How many gallons of a 50% alcohol solution need to be mixed with the 10 gal of the 35% solution to obtain a 40% alcohol solution? 34. A chemist has a 50% acid solution. She needs 30 L of a 15% acid solution. How many liters of water and how many liters of the 50% acid solution should be mixed together to obtain 30 L of a 15% acid solution? 35. A dairy farmer has two types of milk. How many gallons of a 3% milk fat solution and how many gallons of a 4.5% milk fat solution should be mixed to obtain 750 gal of a 4% milk fat solution? 36. How many liters of a 47% hydrochloric acid solution should be mixed with 4 L of a 30% hydrochloric acid solution to obtain a 35% hydrochloric acid solution? For each problem involving distance, rate, and time: (1) use a chart to organize the information, (2) write an appropriate equation, (3) solve the equation, and (4) write the answer in complete sentences. (See Objective 4.) 37. Andy and Brittany live in towns 420 mi apart. They leave their homes at the same time and begin traveling toward one another. Andy travels at 65 mph and Brittany travels at 55 mph. How long will it take before they meet? 38. Two planes leave Chicago’s Midway airport. One plane travels east at 450 mph and the other plane travels west at 600 mph. How long will it take for the planes to be 2310 mi apart? 39. Charlie leaves his home for a meeting traveling at an average rate of 50 mph. After his business meeting is over, he travels back home at an average rate of 70 mph. If his total driving time is 9 hr, how long does he drive going to and from his meeting? What is the total distance Charlie travels?
hendricks_beginning_algebra_1e_ch1_3
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