Transcript Applied Problems: - TCC: Tidewater Community College

Applied Problems:
Mixture and Money
By
Mr. Richard Gill
Dr. Marcia Tharp
Tidewater Community College
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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.
Example 1
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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?
1. Read the problem. A casual guess might
be 250 adult and 350 student tickets.
1.
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 don’t get lost in
your own problem.)
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
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
5. Solve the equation.
5x + 2(600 – x) = 2025
5x + 1200 – 2x = 2025
3x = 825
x = 275
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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PRACTICE PROBLEMS. Then to return
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and continue.
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.
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.
Juan
Amal
Rate
60
72
Time
x
x
Distance
60x
72x
Juan
Rate
60
Time
x
Distance
60x
Amal
72
x
72x
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:
Juan’s distance – Amal’s distance = 30 miles
72x – 60x = 30
12x = 30
x = 2.5 hrs.
It’s your turn to practice.
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