7.2 Applications of Linear Equations

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7.2 Applications of Linear Equations

• Part 1 General Word Problems

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Translating From Words to Mathematical Expressions

• Which mathematical operation does the phrase
  translate into?
• The sum of two numbers
• The difference between two numbers
• The quotient of two numbers
• The product of two numbers
• A number decreased by 12
• A number increased by 5
• Twice a number
• 6 more than a number
• 2 less than a number
• The ratio of two numbers
• ¾ of a number

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Translating into Algebra

• The symbol of equality () is often indicated by
  the word is.
• Translate the following If the product of a
  number and 12 is decreased by 7, the result is
  105.

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? Translate the following

• The sum of a number and 6 is 14
• A number decreased by 18 is -4
• 2/3 of a number is 12

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Applications

• In the 2000 Olympics, US contestants won 14 more
  gold than silver medals. They won a total of 64
  gold and silver medals. How many of each type
  medal were won?

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? The instructions for a woodworking project call
for three pieces of wood. The longest piece must
be twice the length of the middle-sized piece,
and the shortest piece must be 10 inches shorter
than the middle-sized piece. If you want to use
a board that is 70 inches long, how long can each
piece be?
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Mixture and Interest Problems

• Percents often are used in problems involving
  mixing different concentrations of a substance or
  different interest rates.
• In each case, to get the amount of pure substance
  or the interest, we multiply.
• Note In an equation, percents should be written
  as decimals!

Mixture Problems base x rate () percentage
b x r p
Interest Problems principal x rate ()
interest p x r I
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Applications

• If a chemist has 40 liters of a 35 acid
  solution, what is the amount of pure acid in the
  solution?
• If 1300 is invested at 7 simple interest, what
  is the amount of interest earned in one year?

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?Solve each problem.

• How much pure alcohol is in 150 liters of a 30
  alcohol solution?
• If 25,000 is invested at 3 simple interest for
  2 years, how much interest is earned?

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Using Tables to Organize Information

• A chemist needs to mix 20 liters of 40 acid
  solution with some 70 acid solution to get a
  mixture that is 50 acid. How many liters of the
  70 acid solution should be used?

Liters of Solution Rate (as a decimal) Liters of Pure Acid



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? How many liters of a 10 alcohol solution must
be mixed with 40 liters of a 50 solution to get
a 40 solutions?
Strength Liters of Solution Liters of Alcohol