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1.4 Setting Up Equations; Applications

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1.4 Setting Up Equations; Applications. Verbal Description. Language of Math. Mathematical Problem. Real Problem. Solution. Steps for Setting Up Applied Problem. Read the problem. Assign variable(s).

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Presentation Transcript
slide2

Verbal Description

Language of Math

Mathematical Problem

Real Problem

Solution

steps for setting up applied problem
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.
slide4

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

slide5

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

10,000-2,500=7,500.

slide6

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.

slide13

Check.

So it takes 3.68 hours upstream and 2.32 hours

downstream. That is a total of 6 hours.

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