Transcript Math 50 - University of Wisconsin–Stout
Coming Up:
Today:
• • •
Review Quiz 2 Lecture on Section 2.4
: Word problems!
NOTE: This homework is due at the beginning of the next class session.
Coming up at the next three class sessions:
1.
2.
3.
Lecture on Section 2.5
Review for Test 1
Test 1 on Wed. Nov. 5 th (MW) or Thur. 6 th (TTh)
Test 1 on all sections covered this semester up to this point (including material covered on Quizzes 1 and 2, plus sections 2.4 and 2.5)
Gateway Quiz Retake Facts
• •
MUST
pass with
100%
to pass Math 010 So far: Two attempts to pass in class – If not passed during one of those two attempts: • One attempt per week for rest of semester – Eight weeks = eight chances to pass • Outside of class time: scheduled times will be given today and posted on bulletin boards.
Didn’t pass your Gateway Quiz?
• • •
Here are the next steps:
Go over the incorrect answers on your previous attempts with a TA (and get their signature) in the Math TLC Open Lab (JHSW 203).
Take another Practice Gateway Quiz.
– Go over any incorrect answers on the practice attempts with a TA in the Math TLC Open Lab Have a TA in the Math TLC Open Lab sign you up for a retake time
Gateway Quiz Retake Times
(One new attempt allowed per week, beginning October 27) • • Mondays – – 2:30 pm 3:35 pm Tuesdays – 11:15 am – 3:35 pm • • Wednesdays – – 10:10 am 1:25 pm Thursdays – 10:10 am – 11:15 am
SIGN UP IN THE MATH TLC OPEN LAB!
If NONE of the above times work for you… email Krystle Mayer, Math TLC Coordinator (JHSW 201), to set up a date and time.
Online Quiz 2 Results:
•
Average class score after partial credit: __________
•
Commonly missed questions: #_________________ Grade Scale Grade Points
A
≥900 % Score ≥ 90
A-
≥870 ≥ 87
B+
≥840 ≥ 84
B
≥ 800 ≥ 80
B-
≥770 ≥ 77
C+
≥740 ≥ 74
C
≥700 ≥ 70
F
<700 < 70
•If you got less than 70% on Quiz 2, make sure to go over your quiz with me or a TA sometime today or tomorrow to help you prepare for the upcoming midterm test.
Please CLOSE YOUR LAPTOPS,
and turn off and put away your cell phones,
and get out your note taking materials.
Section 2.4: Application Problems:
General strategy for problem solving:
1) 2) 3) 4) 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
Example 1:
The product of twice a number and three is the same as the difference of five times the number and ¾. Find the number.
Understand
-
Read and reread the problem.
- Choose a variable to represent your unknown.
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 .
Example (cont.)
Translate
twice a number The product of and 3 is the same as the difference of 5 times the number and ¾ 2
x
· 3 = 5
x
– ¾
Example (cont.)
Solve
2
x
· 3 = 5
x
– ¾ 6
x
= 5
x
– ¾ (simplify left side) 6
x
+ (-5
x
) = 5
x
+ (-5
x
) – ¾ (add –5
x
to both sides)
x
= - ¾ (simplify both sides)
Now CHECK
your answer (see if both sides produce the same
answer when you put -3/4 in place of x):
Left side
: 2x·3 = (2·-3/4)·3 = -6/4 · 3 = -3/2 · 3= -9/2
Right side:
5x – 3/4 = 5·3/4 – 3/4 = -15/4 – 3/4 = -18/4 = -9/2
Consider the difference between the last problem
: The product of twice a number and three is the same as the difference of five times the number and ¾. Find the number. Equation: 2
x
· 3 = 5
x
– ¾
(Answer = -3/4)
And this problem:
Twice t he product of a number and three is the same as five times the difference of the number and ¾. Find the number.
Equation: 2(
x
· 3) = 5(
x
– ¾)
(Answer = -15/4)
Sample homework problem:
How would you set this problem up?
5(x – 4) = 4 + 5x + 4x
Answer: -6
Example
A car rental agency advertised renting a Toyota Prius for $25 per day and $0.20 per mile. If you rent this car for 2 days, how many miles can you drive on a $100 budget?
Understand
Read and reread the problem.
Just to get an idea of what’s going on in this problems, let’s start by considering what the cost would be if we were to drive a total of 100 miles over the 2 days. In this case our equation for the total cost would come from taking
twice the daily rate
and
adding the fee for mileage
to get
2(25) + 0.20(100)
= 50.00 + 20 =
$70.00.
This gives us an idea of how the cost is calculated, and we also now know that if we have
$100
to spend, we can drive
more than 100 miles
.
Example (cont.)
So to generalize this specific example of 100 miles, if we let
x = the number of miles driven
, then
0.29x = the cost for mileage driven
.
Translate
Daily costs plus mileage costs is equal to maximum budget 2(25) + 0.20
x
= 100
To do this problem without a calculator, we will want to convert the decimal 0.20 into the fraction 20/100.
Example (cont.)
Solve
2(25) + 20/100
x
= 100 50 + 20/100
x
= 100 50
– 50
+ 20/100
x
= 100
– 50
20/100
x
= 50 (simplify left side) (subtract 50 from both sides) (simplify both sides) 100 20 20 100
x
50 100 20
x
= 50∙ 5 = 250 (multiply both sides by 100/20) (simplify both sides)
Example (cont.)
Interpret
Check:
If we replace “number of miles” in the problem with 250, then 50 + 0.20(250) = 50 + 50, which is equal to our budget of $100.
State your answer:
The maximum number of miles we can drive is 250.
Hint: Start by drawing a picture.
Answer: First piece is 4 inches, second is 12, third is 20.
Example:
The sum of three consecutive integers is 366. What are the three integers?
Solution:
•Call the first integer • • •
x + 1
•And the third one?
x + 2 x
+
x + 1
+
x
. •Then what is the next consecutive integer?
•So the sum would be what?
x + 2
• This simplifies to 3x + 3 •And the
equation
would be what?
• 3x + 3 = 366
Example (cont): The sum of three consecutive integers is 366. What are the three integers?
Solution (cont): •Now solve the equation • 3x + 3 = 366 • 3x = 363 • x = 363/3 = 121 •Now answer the question: •First integer = x • • •
x = 121
•Second integer = x + 1
= 122
•Third integer = x + 2
= 123
Example (cont): The sum of three consecutive integers is 366. What are the three integers?
Now check your solution:
(121, 122, 123) •Are these three numbers
integers
?
•Yes •Are they
consecutive
?
•Yes •Do they
add up to 366
?
•
121 + 122 + 123 = 243 + 123 = 366
•
Yes
Example:
Now let’s change the problem slightly: The sum of three consecutive
even
integers is 366. What are the three integers?
Solution:
•Call the first integer
x
. •Then what is the next consecutive
even
•And the third one? • •So the sum would be what? • •
x + 2 x + 4 x
+
x + 2
+
x + 4
• This simplifies to 3x + 6 •And the
equation
would be what?
• 3x + 6 = 366 integer?
Example (cont): The sum of three consecutive even integers is 366. What are the three integers?
Solution (cont): •Now solve the equation • 3x + 6 = 366 • 3x = 360 • x = 360/3 = 120 •Now answer the question: •First integer = x • • •
x = 120
•Second integer = x + 2
= 122
•Third integer = x + 4
= 124
Example (cont): The sum of three consecutive integers is 366. What are the three integers?
Now check your solution:
(120, 122, 124) •Are these three numbers
integers
?
•Yes •Are they
even
?
•Yes •Do they
add up to 366
?
•
120 + 122 + 124 = 242 + 124 = 366
•
Yes
Reminder:
This homework on Section 2.5 is due at start of next class session.
You may want to come in to the lab for help on this homework. Many students find that these problems take a bit longer to figure out than previous assignments.
Also, please remember to come in to the lab for your Gateway quiz review and get your worksheet signed , then
sign up with a TA in the open lab
for one of the time slots for this week’s retake
.
Gateway Quiz Retake Times
(One new attempt allowed per week, beginning October 27) • • Mondays – – 2:30 pm 3:35 pm Tuesdays – 11:15 am – 3:35 pm • • Wednesdays – – 10:10 am 1:25 pm Thursdays – 10:10 am – 11:15 am
SIGN UP IN THE MATH TLC OPEN LAB!
If NONE of the above times work for you… email Krystle Mayer, Math TLC Coordinator (JHSW 201), to set up a date and time.
Note to instructors : The remaining slides contain additional problems from today’s homework that you might want to cover if time allows.