Any questions on Section 2'1

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Any questions on Section 2.1?
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Comment on the 2.1 homework Types of outcomes
when solving linear equations in one variable

• 1. One solution (nonzero). (most problems in 2.1)
• Example 2x 4 4(x 3)
• Solution x -4
• 2. One solution (zero). (as in problems 6 20)
• Example 2x 4 4(x 1)
• Solution x 0
• 3. Solution All real numbers. (as in problems
  15,17,21)
• Example 2x 4 2(x 2)
• Solution All real numbers. (R on computer)
• 4. No solutions. (as in problems 16,18,23)
• Example 2x 4 2(x 3)
• Solution No solution (N on computer)

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Now please CLOSE YOUR LAPTOPS and turn off and
put away your cell phones.
Sample Problems Page Link (Dr. Bruce Johnston)
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Section 2.2

• An Introduction to Problem Solving

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Reminder

• This homework assignment
• on section 2.2 is due
• at the start of
• next class period.
• Make sure you turn in the worksheet showing all
  your work for problems 5 -19 of this assignment.
  
• If you dont turn this in, or if you dont
  completely show your work on any problem/s, your
  online score will be reduced for those 15
  problems out of the 24 total problems in the
  online assignment.)

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Section 2.2

• General strategy for problem solving
• Understand the problem
• Read and reread the problem
• Choose a variable to represent the unknown
• Construct a drawing, whenever possible
• Translate the problem into an equation
• Solve the equation
• Interpret the result
• Check solution
• State your conclusion

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The product of twice a number and three is the
same as the difference of five times the number
and ¾. Find the number.
Read and reread the problem. If we let x the
unknown number, then twice a number
translates to 2x, the product of twice a
number and three translates to 2x 3,
five times the number translates to 5x, and
the difference of five times the number and ¾
translates to 5x - ¾.
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(No Transcript)
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2x 3 5x ¾
6x 5x ¾ (simplify left side)
x - ¾ (simplify both sides)
Now CHECK your answer Left side 2x3
(2-3/4)3 -6/43 -3/23 -9/2 Right side
5x-3/4 53/4-3/4 -15/4 3/4 -18/4 -9/2
? (You can perform this check quickly by using
your calculator.)
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Sample problem from todays homework
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A car rental agency advertised renting a Buick
Century for 24.95 per day and 0.29 per mile.
If you rent this car for 2 days, how many whole
miles can you drive on a 100 budget?
Read and reread the problem. If we let x the
number of whole miles driven, then 0.29x
the cost for mileage driven
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(No Transcript)
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2(24.95) 0.29x 100
49.90 0.29x 100 (simplify left side)
0.29x 50.10 (simplify both sides)
x ? 172.75 (simplify both sides)
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Check Recall that the original statement of the
problem asked for a whole number of miles. If
we replace number of miles in the problem with
173, then 49.90 0.29(173) 100.07, which is
over our budget. However, 49.90 0.29(172)
99.78, which is within the budget. State The
maximum number of whole number miles is 172.
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MATH 110 - Section 2.2 Homework Problem Tip

• If youre having trouble doing percent problems
  that give you a new value after a certain percent
  increase or decrease from an old value (such as
  sales tax problems), try thinking about it this
  way
• Think about when you go shopping to buy, say, a
  TV. Usually you know how much the TV costs, for
  example 400, and the percent tax rate, for
  example 5.5. Normally what you do (or the
  salesclerks computer does) is calculate the
  TOTAL COST by taking 5.5 of 400, then adding
  that amount back onto the 400 price of the TV
  to get the total cost to you.

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• The working equation is
• PRICE TAX TOTAL COST.
• In words, heres what you did (after writing the
  5.5 as a decimal, 0.055)
• PRICE .055 times PRICE TOTAL COST
• Plugging in the numbers, we get
• 400 .055 x 400 400 22 422.
• Notice that youve multiplied the OLD VALUE (the
  price before tax) by the .055.

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• The same basic format applies to anything with a
  percent increase or decrease from an original
  amount
• Old amount /- of old amount new amount
• (Remember to write the percent as a decimal.)
• This equation works for raises in pay, population
  increases or decreases, and many other percent
  change problems, especially where youre given
  the new amount and the percent change and you
  need to work backwards to find out the old amount.

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Example

• After a 6 pay raise, Noras 2005 salary is
  39,703. What was her salary in 2004? (Round to
  the nearest dollar).
• Solution Recall the equation
• Old amount of old amount new amount
• The old amount is her 2004 salary, which is
  unknown, so well call it X.
• This gives us the equation
• X 0.06X 39703

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Example (cont.)

• After a 6 pay raise, Noras 2005 salary is
  39,703. What was her salary in 2004? (Round to
  the nearest dollar).
• X 0.06X 39703
• This simplifies to 1.06X 39703
• Divide both sides X 39703
• by 1.06 to get X. 1.06
  
• Answer Her 2004 salary was 37,456

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Now check your answer

• 37456 .06 x 37456 37456 2247 39703 ?
• NOTE that this DOES NOT give you the same answer
  as if you subtracted 6 of the new salary (39703)
  from the new salary.
• Try it and youll see that it doesnt work.
• (Its not real far off, but enough to give you
  the wrong answer, and the bigger the percentage,
  the farther off youll be.)

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Sample problem from todays homework
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Reminder

• This homework assignment
• on section 2.2 is due
• at the start of
• next class period.
• Make sure you turn in the worksheet showing all
  your work. If you dont turn this in, your online
  score will be reduced. If you dont completely
  show your work on any problem/s, your online
  score will be reduced for those problems.

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You may now OPEN your LAPTOPS and begin working
on the homework assignment.