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2.5

• Formulas and Problem Solving

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Formulas

• A formula is an equation that states a known
  relationship among multiple quantities (has more
  than one variable in it).

A lw (Area of a rectangle
length width) I PRT (Simple
Interest Principal Rate Time) P a b c
(Perimeter of a triangle side a side b
side c) d rt (distance rate
time) V lwh (Volume of a rectangular
solid length width height)
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Using Formulas
Example
A flower bed is in the shape of a triangle with
one side twice the length of the shortest side,
and the third side is 30 feet more than the
length of the shortest side. Find the dimensions
if the perimeter is 102 feet.
1.) UNDERSTAND
Read and reread the problem. Recall that the
formula for the perimeter of a triangle is P a
b c. If we let x the length of the
shortest side, then 2x the length of the
second side, and x 30 the length of the
third side
Continued
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Using Formulas
Example continued
2.) TRANSLATE
Formula P a b c
Substitute 102 x 2x x 30
3.) SOLVE
102 x 2x x 30
102 4x 30 Simplify right side.
102 30 4x 30 30 Subtract 30 from
both sides.
72 4x Simplify both sides.
Continued
18 x Simplify both
sides.
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Using Formulas
Example continued
4.) INTERPRET
Check If the shortest side of the triangle is
18 feet, then the second side is 2(18) 36 feet,
and the third side is 18 30 48 feet. This
gives a perimeter of P 18 36 48 102 feet,
the correct perimeter. State The three sides of
the triangle have a length of 18 feet, 36 feet,
and 48 feet.
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Solving Formulas
It is often necessary to rewrite a formula so
that it is solved for one of the variables.
This is accomplished by isolating the designated
variable on one side of the equal sign.

• Solving Equations for a Specific Variable
• Multiply to clear fractions.
• Use distributive property to remove grouping
  symbols.
• Combine like terms to simplify each side.
• Get all terms containing specified variable on
  the same side, other terms on the opposite side.
• Isolate the specified variable.

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Solving Equations for a Specific Variable
Example
Solve for n.
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Solving Equations for a Specific Variable
Example
Solve for T.
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Solving Equations for a Specific Variable
Example
Solve for P.