Transcript 7.2 Applications of Linear Equations

7.2 Applications of Linear
Equations
Part 1: General Word Problems
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
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.
 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
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?
 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?
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.
Mixture Problems
base x rate (%) = percentage
b
x
r
=
p
Interest Problems
principal x rate (%) = interest
p
x
r
= I
Note: In an equation, percents should be written as
decimals!
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?
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?
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
Liters of
Rate
Liters of
should be used?
Solution
(as a decimal)
Pure Acid
 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