Applied Problems

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Applied Problems

• Mixture and Money
• By
• Mr. Richard Gill
• Dr. Marcia Tharp
• Tidewater Community College
• Click to view.

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Introduction
We are going to use a six- step process for
solving Mixture and Money Problems. The steps are
1) Read the problem.
2) Define x.
3) Name the unknown quantities in terms of x.
4) Form an equation.
5) Solve the equation.
6) Check to see if you answered the question.
Now lets go on and see how this works in a
problem.
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Example 1Print this page.

• The Hurrah Players sold 600 tickets to a recent
  event. Adults paid 5 each and students paid 2
  each. If the total collected was 2025, how many
  tickets of each type were sold?

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• Read the problem. A casual guess might be 250
  adult and 350 student tickets.

• 2. Define x. Let x answer the question. In
  other words, let x equal the number of adult
  tickets sold.
• x the number of adult tickets.
• (It would be OK to let x equal the number
  of student tickets but, of course, x cannot be
  both things simultaneously. It is very important
  to write down your definition of x so that you
  dont get lost in your own problem.)

1.
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• 3. Name other unknown quantities in terms of x.
  This is usually the crucial step in the solution.
  In money problems, it is very important to
  remember that the number of tickets and the value
  of the tickets are two different quantities.

600 x the number of student tickets. 5x the
amount of money from adult tickets (5 per
ticket) 2(600 x) the amount of money from
student tickets
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• 4. Form the equation. The money from the
  student tickets and the money from the adult
  tickets should add up to equal the total amount
  collected.

cost student tickets cost adult tickets total
collected
5x 2(600 x) 2025
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• 5. Solve the equation.

5x 2(600 x) 2025
5x 1200 2x 2025
3x 825
x 275
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• 6. Answer the question.
• We have answered the first part of the
  question since we defined x as the number of
  adult tickets sold. To find the number of student
  tickets sold we need only to calculate the value
  of 600 x.
• x 275 the number of adult tickets sold
• 600 x 325 the number of student tickets
  sold
• 600- 275 375

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• Its your turn!Click below to do PRACTICE
  PROBLEMS. Then to return
• click the back button on your browser and
  continue.

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Applied Problems Motion

• Example 2
• Motion problems use the equation
• D RT
• where D is the distance traveled,
• R is the rate of travel and
• T is the time spent traveling.
• It is helpful to use a D RT grid when solving
  motion problems as shown in the following
  example.

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• Juan and Amal leave DC at the same time headed
  south on I-95. If Juan averages 60 mph and Amal
  averages 72 mph how long will it take them to be
  30 miles apart?
• Now would be a good time for a guess. Write
  yours down and compare it to the answer you get
  algebraically.

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• The purpose of the grid is to find an algebraic
  name for each distance. Notice that the distance
  30 miles does not appear in the grid because
  neither Juan nor Amal traveled 30 miles. Notice
  also that we could use x for each time since Juan
  and Amal were on the road for the same amount of
  time. We will need to work 30 miles into the
  equation as follows

Juans distance Amals distance 30 miles
72x 60x 30
12x 30
x 2.5 hrs.
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• Its your turn to practice.
• Click here.