Use percent in problems involving rates'

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2.7 More about Problem Solving

• 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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• 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

3

• 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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• 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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• 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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• 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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• 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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• 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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• Solve problems involving distance, rate, and time
• Let d distance
• r rate
• t time
• Then
• d rt r d / t t d / r

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• 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