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Connections among
Representatives
Horses and Birds
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Horses and Birds
Marie’s family went to Kentucky for their vacation.
While in Kentucky, Marie noticed there were many
horse farms. To occupy her time while the family
was touring the countryside one day, Marie kept a
total of the number of legs on the horses and birds
in each pasture. At the end of the day, Marie asked
her sister Michelle how many horses and how many
birds had Marie counted if she counted a total of
284 legs. Michelle was able to quickly calculate the
number of horses and the number of birds. Marie
asked Michelle how she was able to do this so
quickly. Michelle simply stated, “I used patterns and
math.” Develop a strategy to determine the number
of horses and birds if Marie counted a total of 284
legs.
Horses and Birds
Each horse has ________ legs
Each bird has ________ legs
h number of legs for horses
b number of legs for birds
What equation can we use to represent the number of
legs for more than one horse or bird
H*4=
B*2=
If we count 54 legs total our equation should be?
4h + 2b = 54 legs
Notes
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Variable:
 a symbol, usually a
letter that
represents one or
more numbers. Any
letter may be used
as a variable
Mathematical
expression:
 consists of numbers,
variables, and
operations
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To evaluate a
mathematical
expression,
substitute the
given numeric
value in for the
variable and
perform the given
operation.
Examples
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The sum of a number and 10
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The difference of a number and 21
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48/n
The product of 6 and a number
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n – 21
The quotient of 48 and a number
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n + 10
6n
One forth of a number
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1/4n
Evaluating
Evaluate the variable expression
3x - 5y, if x = 7 and y = 4.
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Substitute 7 for x and 4 for y. Put substituted values
in parentheses. 3(7) – 5(4)
• Simplify the resulting expression using order
of operations.
3(7) – 5(4)
21 – 5(4)
21 – 20
=1
Evaluate the each expression below if
a = 6.2 and b = (− 9).
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a. 8a
8(6.2)
= 49.6
b. ab
(6.2) (− 9)
= (−55.8)
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c. b(a – 3)
(−9)(6.2 – 3)
= (−28.8)
d. 6b2
6(−9)2
6(81)
= 486
Example 1
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An electrician charges $45 per hour,
plus $50 for the service call. Let x
represent the number of hours
worked.
Equation

45x + 50
Example 2
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The number of freshmen is ¼ of the
number of total students. Let x
represent the number of freshmen
and n is the total number of
students.
Equation
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n*¼=x
¼ is also equal to 0.25
Example 3
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The number of hours, x, worked at
$15 an hour is the total pay, y.
Equation

y = 15x
Your work!
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1.
7(8 + 4) =
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2.
6(x – 7) =
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3.
3(4x – 5) =
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4.
12(4y + 12) =
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5.
1/5(x – 35) =
Distributive Property:
distributing something as you separate or break it into parts. The distributive
property makes numbers easier to work with, you are distributing.
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1. 4(y + 9) =
2. 3(x + 4) =
3. 2(x + 3) =
4. 4(y + 12) =
5. 4(n + 5) =
6. 2(2n – 6) =
7. 4(x + 14) =
8. 12(x + 4) =
9. 5(x + 3) =
10. 3(y + 13) =
http://www.youtube.com/watch?v=EixCbmu8GiY
Word Problems
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11. The students in Mrs. Lane's class are building
balloon-powered cars for a Mathematics
project. Each student needs a balloon that
costs $0.05, a package of wheels for $1.00,
and a car frame kit for $1.50. Which equation
can be used to find y, the amount in dollars,
spent by all of Mrs. Lane's students, as related
to x, the number of students in Mrs. Lane's
class?
A. y = ($0.05 + $1.00 + $1.50)
B. y = $2.55x
C. y = $2.55 + x
D. y = $3.00x
Word Problems
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12. Which expression is equivalent
to the sum of 3 times a number and
6?
A 3x + 6
B 3(x + 6)
C x(3+6)
D 3 + 6x
Word Problem
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13. Which of the following
represents the algebraic expression
6 less than a number n?
A6÷n
B6–n
Cn–6
Dn+6