Transcript Section 3.4 and 4.1

Section 3.4
3.4 Translating
Sentences in Equations
• You already know how to do most of
this!
• Same as section 2.3
• But a few new add-ons (just a few)
How do I do these again?
• 1. Assign a variable to the unknown
number
• 2. Find two verbal expressions for the
same value
• 3. write the math expression for each
verbal expression
• 4. Write in the equals sign
• 5. Solve it!
Many words for the same
thing
• The Inuit's have over 20 words for snow
• We have 5 ways to say this symbol “=“
•
•
•
•
•
Equals
Is
Is equal to
Amounts to
Represents
How its used
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Translate “five less than a number is thirteen”
Five less than a number------is------thirteen
The number : n
Five less than a number: n-5
Thirteen: 13
n-5 = 13
Or
Spongebob sez:
•The sum of two numbers in sixteen.
The difference between four times
the smaller number and two is two
more than twice the larger number.
Find those two numbers!
• Smaller number: n
• Bigger number: 16-n
The difference
between four times
the smaller and two
Is
Two more than
twice the large
4n – 2 = 2(16-n) +2
Example 2: The real world
• You go into a ritzy night
club and it costs $25 for
all of you just to get in. In
an attempt to impress your
date, you decide that you
will buy the “beverages*”
for the group. Each round
of beverages costs you $12
dollars. If your total bill
including your entrance fee
and all the rounds is $97,
how many rounds did you
buy?
•
*no alcohol
• Each round: n
• $25 entrance
fee plus $12 for
each round
• is
• $97
25 + 12*n = 97
You Try It
• The sum of two numbers is twentyfive. The total of four times the
smaller number and two is six less
than the product of two and the
larger number. Find the two numbers
• 4x+2=2(25-x)-6
• 7,18
Even, Odd, and
consecutive
•Even integer—a number divisible by 2
•Like 4
•Odd integer – a number not divisible by 2
•Like 5
•Consecutive integers -- integers that follow one another in order
•Like: 101, 102, 103 or -5, -4, -3 or x, x+1, x+2
•Consecutive even integers: 2, 4, 6
or y, y+2, y+4
•Consecutive odd integers: 11, 13, 15, or n, n+2, n+4
•Variable representation is the same for consecutive odd or even why?
Examples
• Sum of three consecutive odd
integers is 45. Find ‘em.
• First odd integer: n
• Second odd integer: n+2
• Third odd integer: n+4
• The sum of these is 45
You try it NOW!
• The sum of two numbers is twelve. The
total of three times the smaller number
and six amounts to seven less than the
product of four and the larger numbers.
Find the two numbers!
• 5, 7
• Find three consecutive integers whose sum
is negative six
• -3,-2,-1
• Happy Thanksgiving
• Being the great chef you
are, you cooked a 20 foot
long bird for Thanksgiving.
You cut it into two pieces
to make it fit on the table.
Five times the length of
the shorter piece is 2 ft
more than twice the length
of the longer piece. The
length of each piece.
• Shorter piece: x
• Longer piece: 20 –x
– The shorter piece is usually the variable and
the longer is the total minus the shorter piece
(i.e. what is left).
• For difficult problems  Draw it out!
• Five times the
length of the
shorter piece
• is
• 2 ft more than
twice the length
of the longer
• 5x = 2(20 –x) +2
You try this
• A piano wire 24 in. long is cut into two pieces. The
longer piece is 4 in. more than three times the
shorter piece. Find the length of each piece.
• 5 in., 19 in.
• An Electric company charges $0.07 for each of
the first 249 kWh (kilowatt-hours) and $.14 for
each kilowatt-hour over 249 kWh. Find the
number of kilowatt-hours used by a family whose
electric bill was $28.77
• 330 kwh
Homework 3.4
• 1 thru 41 EOO
• 12, 22, 30, 40, 44