Transcript 3.1 Writing Equations

3.1 Writing Equations
WARM UP
Write the following verbal expressions as
algebraic expressions:
1) The difference of twice a number x and 4.
2) 3 times a number y less than twice the sum
of a number x and 5
Write the following algebraic expressions as a
verbal expression.
3) 3 + 4n
4) 5 (x + 1) – 12
What is the difference
between writing an algebraic
expression and writing an
equation?
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Requires having equality in an
equation or equals sign to say two
expressions are the same
Equations have = signs
Expressions do not (2 expressions can
become an equation)
Translate each sentence into
an equation.
1) Five times the number a is equal to three time
5a = 3(b+c)
the sum of b and c.
2)
Nine times y subtracted from 95 equals 37.
95 – 9y = 37
3) The product of five and the sum of m and n is
the same as seven times n. 5(m + n) = 7n
4) Two times a number t decreased by 8 is identical
to seventy.
2t – 8 = 70
Four-Step Problem Solving Plan
EXAMPLE: Today, 2,000,000 gallons of
ice cream are produced in the United States
each day. How many days can 40,000,000
gallons of ice cream be produced in the
United States?
STEP 1: EXPLORE THE PROBLEM
•Read the problem carefully
•Identify what information is
given
•Identify what you are asked to
find
STEP 2: PLAN THE SOLUTION
•Choose a strategy to solve the
problem
STRATEGY #1: Write an Equation:
•Define a Variable: choose
a variable (letter) to represent
unknown numbers in the
problem
Know: 2,000,000 gallons
of ice cream are produced
in US each day.
Want to Know: how many
days it will take to produce
40,000,000 gallons of ice
cream
Let d represent the number
of days needed to produce
the ice cream.
2,000,000 * d = 40,000,000
STEP 3: SOLVE THE PROBLEM
•Use the strategy from
Step 2 to solve the
problem
“What number of times
2,000,000 =
40,000,000?”
2,000,000d = 40,000,000
d = 20
STEP 4 EXAMINE THE SOLUTION
20 days makes sense
•Check your solution in
relation to the original
problem
•Does it make sense?
•Does it fit the information in
the problem?
Formulas
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specific type of equation that states
a rule for the relationship between
certain quantities
For formulas it’s important to identify all
the variables.
You are defining a variable
Using known quantities with formulas we
can plug them in to find others
Translate each sentence into a formula:
1) The area of a triangle is equal to one half times the base
times the height.
A = ½ bh
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a. What is the area of a triangle with base 4 and height 11?
A = 22
2) The perimeter of a rectangle equals two times the length
plus two times the width.
P = 2l + 2w
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a. What is the perimeter of a rectangle with base 5 and height 7?
P = 24
Practice
3) The volume of a rectangular prism (box) is the same as
the product of the length, the width, and the height.
V = lwh
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a. What is the volume of a triangle with length 4, width 3
and height 5?
V = 60
4) The volume V of a sphere is four-thirds times  times the
radius r of the sphere cubed.
V = 4/3  r3
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a. What is the volume of a sphere with radius of 4?
V =85.33