Transcript Beginning & Intermediate Algebra. 4ed

§ 2.5
Formulas and
Problem Solving
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)
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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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
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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
102 – 30 = 4x + 30 – 30
Simplify right side.
Subtract 30 from both sides.
72 = 4x
Simplify both sides.
72 4 x

4
4
Divide both sides by 4.
18 = x
Simplify both sides.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
Continued
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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.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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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
1)
2)
3)
4)
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.
5) Isolate the specified variable.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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Solving Equations for a Specific Variable
Example:
Solve for n.
T  mnr
T
mnr

mr
mr
Divide both sides by mr.
T
n
mr
Simplify right side.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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Solving Equations for a Specific Variable
Example:
Solve for T.
A  P  PRT
A  P  P  P  PRT
Subtract P from both sides.
A  P  PRT
Simplify right side.
A  P PRT

PR
PR
Divide both sides by PR.
A P
T
PR
Simplify right side.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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Solving Equations for a Specific Variable
Example:
Solve for P.
A  P  PRT
A  P(1  RT )
Factor out P from both terms on the
right side.
A
P(1  RT )

1  RT
1  RT
Divide both sides by 1 + RT.
A
P
1  RT
Simplify the right side.
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