1.4 Setting Up Equations; Applications

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1.4Setting Up Equations Applications
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Verbal Description
Language of Math
Mathematical Problem
Real Problem
Solution
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Steps for Setting Up Applied Problem

• Read the problem.
• Assign variable(s).
• Make a list of known facts, translate them into
  mathematical expressions. If possible sketch the
  situation.
• Solve the equation for one variable, and then
  answer the question.
• Check your answer.

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A total of 10,000 is invested, some in stocks
and some on bonds. If the amount invested in
bonds is three times the amount invested in
stocks, how much is invested in each category?
Let x denote the amount invested in stocks. Then
10,000 - x is the amount invested in
bonds. Total amount in bonds three times the
stocks 10,000 - x 3x
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10,000 - x 3x 10,000 4x x
2,500
The total amount invested in stocks is 2,500.
The total amount invested in bonds is
10,000-2,5007,500.
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A motor boat heads upstream a distance of 50
miles on Fraser River, whose current is
running at 4 miles per hour. The trip up and back
takes 6 hours. Assuming that the motorboat
maintained a constant speed relative to the
water, what was its speed?
Denote v - velocity of the boat.
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Set up a table.
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The total time traveled is 6 hours. We get
Solve this for v.
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(No Transcript)
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Solve by using a quadratic formula.
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(No Transcript)
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The negative answer does not make sense, so we
have the velocity
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Check.
So it takes 3.68 hours upstream and 2.32 hours
downstream. That is a total of 6 hours.