verify unit of measure in a multivariate equation © 20111
TRANSCRIPT
Verify Unit of Measure in a Verify Unit of Measure in a Multivariate EquationMultivariate Equation
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You can’t….You can’t….
+ = ??
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Terminal Learning ObjectiveTerminal Learning Objective
• Task: Determine Unit of Measure in a Multivariate Equation
• Condition: You are training to become an ACE with access to ICAM course handouts, readings, and spreadsheet tools and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors
• Standard: with at least 80% accuracy:• Describe mathematical operations using units of measure
• Solve unit of measure equations• Describe key cost equations
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Importance of Units of MeasureImportance of Units of Measure
• You can’t add apples and oranges but you can add fruit
• Define the Unit of Measure for a cost expression
• Use algebraic rules to apply mathematical operations to various Units of Measure
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AddingAdding• If two components of the cost expression have the
same unit of measure, they may be added together
• Example: Smoky Mountain InnDepreciation on building $60,000 per yearMaintenance person’s salary $30,000 per yearCleaning person’s salary $24,000 per yearReal estate taxes $10,000 per year
• Depreciation, maintenance, cleaning, and taxes are all stated in $ per year, so they may be added to equal $124,000 per year
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AddingAdding
• If two components of the cost expression have the same unit of measure, they may be added together
• Example: Smoky Mountain InnLaundry service $4.00 per person-nightFood $6.00 per person-night
• Laundry and food are both stated in $ per person-night, so they may be added to equal $10 per person-night
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SubtractingSubtracting
• If two components of the cost expression have the same unit of measure, they may be subtracted
• Example:• Selling price is $10 per widget• Unit cost is $3.75 per widget• Since both Selling price and Unit cost are stated in
$ per widget, they may be subtracted to yield Gross Profit of $6.25 per widget
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DividingDividing
• “Per” represents a division relationship and should be expressed as such
• Example:• Cost per unit = Total $ Cost / # Units• Total Cost = $10,000• # Units = 500• $10,000/500 units = $20/unit
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CancellingCancelling
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MultiplicationMultiplication
• When multiplying different units of measure, they become a new unit of measure that is the product of the two factors
• Example:• 10 employees * 40 hrs = 400 employee-hrs• 2x * 3y = 6xy
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Cross-CancellingCross-Cancelling
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FactoringFactoring
• If the same unit of measure appears as a factor in all elements in a sum, it can be factored out
• Example:• $4/hour + $6/hour = • $/hr *(4 + 6)
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Learning CheckLearning Check
• If two components of a cost expression have the same unit of measure, they may be either
or .• Which mathematical operation using two
different units of measure results in a new unit of measure?
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Proving a Unit of MeasureProving a Unit of Measure
• What is the cost expression for a driving trip?• The cost will be the sum of the following
components:$ Gasoline + $ Insurance + $ Driver’s time
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Variables Affecting Cost of TripVariables Affecting Cost of Trip
• All of the following items will affect our trip’s cost:• Distance in miles (represented by x)• Gas usage in miles per gallon (represented by a)• Cost per gallon of gas in dollars (represented by b)• Insurance cost in dollars per mile (represented by c) • Driver’s cost in dollars per hour (represented by e)• Average speed in miles per hour (represented by d)
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Cost of GasolineCost of Gasoline
• Cost of gasoline = # gallons * $/gallon• # gallons = x miles ÷ a miles/gallon • When dividing fractions, invert the second
fraction and multiply• Cost of gasoline =• x miles * gallon /a miles * b $/gallon
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Cost of InsuranceCost of Insurance
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Cost of Driver’s TimeCost of Driver’s Time
• Cost of Driver’s Time = # hours * $/hour• # hours = x miles ÷ d miles/hour• Or: x miles * hour/d miles• Hours/mile * $/hour * miles on trip• So:• hours/d mile * e $/hour * x miles
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Cost ExpressionCost Expression
gallon/ a miles * x miles * b $/gal+
c $/mile * x miles+
hours/d mile * e $/hour * x miles
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Proving the Unit of MeasureProving the Unit of MeasureCost of Gasoline + Cost of Insurance + Cost of Driver’s Time
x miles * gallona miles
* b $gal
+ c $mile
* x miles + hourd miles
* e $hour
* x miles
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Proving the Unit of MeasureProving the Unit of MeasureCost of Gasoline + Cost of Insurance + Cost of Driver’s Time
x miles * gallona miles
* b $gal
+ c $mile
* x miles + hourd miles
* e $hour
* x miles
x miles * ( Cost of Gasoline/mile + Cost of Insurance
/mile + Cost of Driver’s Time /mile )
x miles * ( gallona miles * b $
gal+ c $
mile + hourd miles * e $
hour )
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Proving the Unit of MeasureProving the Unit of Measure
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Proving the Unit of MeasureProving the Unit of Measure
x miles * ( Cost of Gasoline/mile + Cost of Insurance
/mile + Cost of Driver’s Time /mile )
x miles * ( b a * $
mile + c * $mile + e
d * $mile )
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Plugging Values into the EquationPlugging Values into the Equation
$ * x * ( b a + c + e
d )
What is the cost of the trip if:The distance (x) is 300 milesThe car gets 25 miles per gallon (b)The cost of a gallon of gas is $4The insurance cost per mile (c) is $.05The driver’s cost per hour is $20 (e)The average speed is 80 miles per hour (d)
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Plugging Values into the EquationPlugging Values into the Equation
$ * x * ( b a + c + e
d )$ * 300 * ( 4
25 + .05 + 2080 )
What is the cost of the trip if:The distance (x) is 300 milesThe car gets 25 miles per gallon (a)The cost of a gallon of gas is $4 (b)The insurance cost per mile (c) is $.05The driver’s cost per hour is $20 (e)The average speed is 80 miles per hour (d)
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Learning CheckLearning Check
• What is the procedure when dividing by a fractional unit of measure?
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The Value of EquationsThe Value of Equations
• Equations represent cost relationships that are common to many organizations
• Examples:• Revenue – Cost = Profit• Total Cost = Fixed Cost + Variable Cost• Beginning + Input – Output = Ending
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Input-Output EquationInput-Output Equation
Beginning + Input – Output = End
If you take more water out of the bucket than you put in,
what happens to the level in the bucket?
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Applications of Input-OutputApplications of Input-Output
• Account Balances• What are the inputs to the account in
question?• Raw materials?• Work In process?• Finished goods?• Your checking account?
• What are the outputs from the account?
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Applications of Input-OutputApplications of Input-Output
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Using the Input-Output EquationUsing the Input-Output Equation
• If any three of the four variables is known, it is possible to solve for the unknown
• The beginning balance on your credit card is $950. During the month you charge $300 and make a payment of $325. At the end of the month your balance is $940. What was the finance charge?
• What are the inputs? Charges and finance charge• What are the outputs? Payments
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Using the Input-Output EquationUsing the Input-Output Equation
• If any three of the four variables is known, it is possible to solve for the unknown
• The beginning balance on your credit card is $950. During the month you charge $300 and make a payment of $325. At the end of the month your balance is $940. What was the finance charge?
• What are the inputs? Charges and finance charge• What are the outputs? Payments
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Using the Input-Output EquationUsing the Input-Output Equation
• Set up the equation:Beginning + Inputs – Outputs = Ending
Beg + Charges + Finance Charges – Payments = End$950 + $300 + Finance Charge – $325 = $940
$1250 + Finance Charge – $325 = $940$925 + Finance Charge = $940Finance Charge = $940 – $925
Finance Charge = $15
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Using the Input-Output EquationUsing the Input-Output Equation
• Set up the equation:Beginning + Inputs – Outputs = Ending
Beg + Charges + Finance Charges – Payments = End$950 + $300 + Finance Charge – $325 = $940
$1250 + Finance Charge – $325 = $940$925 + Finance Charge = $940Finance Charge = $940 – $925
Finance Charge = $15
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Using the Input-Output EquationUsing the Input-Output Equation
• Set up the equation:Beginning + Inputs – Outputs = Ending
Beg + Charges + Finance Charges – Payments = End$950 + $300 + Finance Charge – $325 = $940
$1250 + Finance Charge – $325 = $940$925 + Finance Charge = $940Finance Charge = $940 – $925
Finance Charge = $15
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Using the Input-Output EquationUsing the Input-Output Equation
• Set up the equation:Beginning + Inputs – Outputs = Ending
Beg + Charges + Finance Charges – Payments = End$950 + $300 + Finance Charge – $325 = $940
$1250 + Finance Charge – $325 = $940$925 + Finance Charge = $940Finance Charge = $940 – $925
Finance Charge = $15
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Using the Input-Output EquationUsing the Input-Output Equation
• Set up the equation:Beginning + Inputs – Outputs = Ending
Beg + Charges + Finance Charges – Payments = End$950 + $300 + Finance Charge – $325 = $940
$1250 + Finance Charge – $325 = $940$925 + Finance Charge = $940Finance Charge = $940 – $925
Finance Charge = $15
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Using the Input-Output EquationUsing the Input-Output Equation
• Set up the equation:Beginning + Inputs – Outputs = Ending
Beg + Charges + Finance Charges – Payments = End$950 + $300 + Finance Charge – $325 = $940
$1250 + Finance Charge – $325 = $940$925 + Finance Charge = $940Finance Charge = $940 – $925
Finance Charge = $15
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Using the Input-Output EquationUsing the Input-Output Equation
• Set up the equation:Beginning + Inputs – Outputs = Ending
Beg + Charges + Finance Charges – Payments = End$950 + $300 + Finance Charge – $325 = $940
$1250 + Finance Charge – $325 = $940$925 + Finance Charge = $940Finance Charge = $940 – $925
Finance Charge = $15
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Learning CheckLearning Check
• What are three useful equations that represent common cost relationships?
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Practical ExercisesPractical Exercises
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