Applied Problems:

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Applied Problems

• Math 8a

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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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Im ready to get this problem done so algebra is
going to be a lot quicker than guessing.
Lets chart the information as follows
This is the information I have!
How many
Value of
Total
Tickets
5
Adult
Student
2
Total
600
2025
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Now lets add the algebra. Since the number of
adult tickets is unknown, let of adult tickets
x
How would we represent the number of student
tickets?
If you said x, that would make x 300
automatically since x also represents adult
tickets. Not right.
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How would we represent the number of student
tickets?
When you know a total (600) and x represents part
of that total, use subtraction total - part 600-x
number of student tickets.
600 - x
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Now we must multiply how many by value of and
put in total column.
5x
2(600 - x)
600 - x
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• Yolanda has dimes and quarters totaling 5.25. If
  she has 33 coins in all how many of each does she
  have?
• Tony has 39 bills in fives and tens. If the total
  value is 285 how many of each does he have?
• 3. The Drama Club sold 500 tickets to their fall
  performance. The adult tickets were 5 each and
  the student tickets were 3 each. If they took in
  2080, how many of each did they sell?

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PRACTICE

• 4. Edie has 27 coins in dimes and quarters. If
  the total value is 3.75 how many of each does
  she have?5. Venus bought 40 stamps for 12.40.
  Some of the stamps were 33-cent stamps and some
  were 23 cent stamps. How many of each did she buy
• 5. Venus bought 40 stamps for 12.40. Some of the
  stamps were 33-cent stamps and some were 23 cent
  stamps. How many of each did she buy?

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PRACTICE

• 6. Sonia has 26 bills in ones and fives. If their
  total value is 50 how many of each does she have

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ANSWERS

• 1. 20 dimes and 13 quarters 
• 2. 21 fives and 18 tens
• 3. 290 adults  and 210 students
• 4. 20 dimes and 7 quarters. 
• 5. 32 stamps at 33 cents each  and 8 stamps at 23
  cents each 
• 6. 20 one dollar bills  and 6 five dollar bills