Solving for the Unknown; a How-to approach to Solving ...
Transcript of Solving for the Unknown; a How-to approach to Solving ...
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Solving for the Unknown; a How-
to approach to Solving Equations
Chapter 5
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If no number is in front of a letter, it is
a 1.
B = 1B
C = 1C
If no sign is in front of a letter or
number, it is a + (positive value)
C = +C
4 = +4
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Whatever you do to one side of an
equation, you must do to the other
Side (unless you are just
combining terms).
Solving for the Unknown Rule
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Equation Equality Rule
You can add the same quantity or number to
both sides of the equation and subtract the
same quantity or number from both sides of
the equation without affecting the equality of
the equation.
You can also divide or multiply both sides of
the equation by the same quantity or number
(except 0) without affecting the equality of the
equation.
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A + 8 = 58
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Subtract 8 from Both Sides
A + 8 = 58
- 8 - 8
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That leaves one A that equals 50
A + 8 = 58
- 8 - 8
A = 50
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Opposite Process Rule
If an equation indicates a process
such as addition, subtraction,
multiplication, or division, solve for
the unknown or variable by using the
opposite process.
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4Y = 28
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4Y = 28
4 4
You can divide 4 into the 4 on the left of the
equation as well as the 28 on the right side of
the equation.
So…
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4Y = 28
4 4
1Y = 7
or
Y = 7
Divide each side by
4 to find out how
much one Y is.
One Y is worth 7
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Multiple Processes Rule
When solving for an unknown that
involves more than one process,
do the addition and subtraction
before the multiplication and division.
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X + 5 = 50
9
X + 5 = 50
9 -5 -5
X = 45
9
X * 9 = 45(9)
9
X = 405
Subtract 5 from both sides
Original equation
Left after subtracting 5 from
both sides
Multiply each side by 9
After multiplying each side
by 9
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When equations contain parentheses, (), which indicates
grouping together, you solve for the unknown by first,
multiplying each item inside the parentheses by the
number or letter just outside the parentheses.
Then you continue to solve for the unknown with the
opposite process used in the equation.
Do the addition and subtractions first, then the
multiplication and division.
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Math Inside the Parentheses First
4(3F - 2) = 64
12F - 8 = 64
12F - 8 64
+ 8 = + 8
12F = 72
12F 72
12 12
F = 6
=
Multiply inside parentheses first
Add 8 to both sides
Divide both sides by 12
Solution-Unknown F equals 6
Result of multiplication
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To solve equations with like
unknowns, you first combine
the unknowns and then solve
with the opposite process
used in the equation.
3Y-Y = 52
Like terms are the two Ys
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3Y - Y = 52 original equation
2Y = 52 combining
unknowns (Y)
2Y = 52 divide by 2
2 2
Y = 26 solution
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Solving Word Problems for Unknowns
1) Read the entire
problem.
2) Ask: “What is the
problem looking for?
3) Let a variable
represent the
unknown
4) Visualize the
relationship
between the
unknowns and
variables. Then set
up equation
5) Check your
results
C = Computers
4C + C = 600
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Situation 1
Wal-mart reduced the price for a radio-alarm by $30.
The sale price is now $50. What was the old price?
P = Price
P–30 = 50
+30 +30
P = 80
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Situation 2
Tribble spends ¼ of his allowance on toy
mice. He spends $2 on these mice. How
much is his allowance? A=allowance
¼ A = 2
4(¼ A) = 4( 2)
A = 8
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Situation 3
John and Fumiko sell computers. John sells 3 times as
many computers as Fumiko. The difference is 20. How
many computers do they each sell? F = Fumiko
3F – F = 20
2F = 20
2F/2 = 20/2
F = 10
Fumiko sells 10 and John sells 30. He sells 3 times as
many as she does, and the difference is 20.
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Situation 4
John sells 3 times as many computers as Fumiko. The
total number of computers sold is 40. F=Fumiko
F + 3F = 40
4F = 40
4F/4 = 40/4
F = 10
Fumiko’s sales + 3 times her sales = 40
Combining unknowns
Dividing both sides by the same number
Unknown is solved
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Situation 5
•Lakers jerseys sell for $81 each and Clippers
jerseys for $6 each.
•Total sales were $498.
•People bought 3 times as many Lakers jerseys
as Clippers jerseys.
A. How many of each were sold?
B. What were the total dollar sales of each?
Solve for number of Clippers jerseys sold first, C.
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# of Price
Jerseys per
Product Sold * Jersey = Total sales
Clippers jerseys C * $6 = $ 6C
Lakers jerseys 3C * $81 = $ 243C
Information Grid on Jersey Sales
The variable C = the number of
Clippers jerseys sold
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$243C + $6C = $498 (total sales)
$249C = $498 (total sales)
$249C = $498
249 249
C = 2 [Clippers jerseys] $6 = $12 of sales)*
Combine the like terms
Finding out how
much 1 C is worth
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Remember that three times more Lakers jerseys
were sold than Clippers jerseys.
3 times the 2 Clippers jerseys (C) = 6 Lakers jerseys
6 Lakers jerseys times $81 each = $486 of sales
Proof
6 Lakers jerseys * $81 = $486
+ 2 Clippers jerseys * $6 = + 12
$498
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