APU MATH110 WEEK 2 AND 3 FORUM

WEEK 2 FORUMOpen the attached file. Pick ONE of the questions that has not already been answered by a classmate. Click on Start a New Conversation
and make the problem number and the topic (#1 Highway Grade) the
subject of your post, so that people can tell at a glance which problems
have already been answered.

In at least 250 words,
give a full and complete answer to the question. I would like you to
find out about the material and describe the answer in your own words.
Most of these topics require some research. Don’t forget that you must
give attribution to your source. Be sure to cut and paste the URL of the
site from which you got the information. Sometimes other students
decide that a topic is interesting and would like to learn more about
it. Your source will provide them with a good starting point. This
initial post is worth 6 points.

You
must also give a substantive response of at least 50 words to two
classmate’s posts (worth 2 points each). You may ask questions to elicit
a more in-depth explanation, add additional information to your own
posting in response to questions, share additional knowledge on another
posting or share an example from your own life related to the topic.
Simply saying “Good post!” will not earn any points.
When you answer these, please incorporate enough
of the question so that we all can tell what you’re talking about without
having to open this file.

Simply saying “#40 All of them” is not very informative!

GRADE

1. What is meant by the grade of a highway?

2. How might the grade of a highway influence the
prices set by trucking companies to haul freight over the route?

3. What is a runaway truck ramp?

4. Why are residential roads higher in the middle than at the curb?
5. What is the generally accepted maximum grade for
wheelchair ramps?

6. What is an adhesion railroad?
7. What is the maximum grade that an adhesion
railroad can climb?

8. What are some of the steepest adhesion
railroads in the world and where are they located? (just give us one and leave
the others for classmates!)

9. What is a cog railway?
10. Where is the world’s highest cog railway?

11. Where is the world’s steepest cog railway?
12. How does a “rack-and-adhesion” railway
work?

13. Name 2 types of transportation that are frequently called cable cars?

14. How do the San Francisco cable cars work?

15. How can canals be used to help boat climb hills?
16. How does a canal lock work?

17. How high above sea level is Lake Gatun in the Panama Canal?

PITCH

18. How steep does a roof have to be to be considered “pitched”?
19. What distinguishes a “salt box” house?

20. What distinguishes an A-frame house?
21. You may have read Anne of Green Gables – what’s
a gable?

22. Why are gable end roofs among the worst roof designs for hurricane
regions?
23. What are some advantages & Disadvantages of
a Dutch Hip Roof Style?

24. Why are roof lines different in New England and the Southwest?
25. About how steep is the average residential staircase?

SLIPPERY SLOPES

26. About how steep is the angle of the slope for “Extreme Skiers”?

27. In the US, about how steep is a green, beginners’ slope?
28. In the US, about how steep is a blue,
intermediate slope?

29. In the US, about how steep is a black, expert
slope?

30. I can ski a double black diamond slope at home
in Indiana. I can’t wait to ski one in Colorado! Is this wise? Why?WEEK 3 3: If Only I Had a System
Read
the attached files. First read the one entitled “MATH110 Read this
first,” and then open the file called “Systems of Equations
Problems with Answers.”

Pick ONE of the problems that has not already been solved, and demonstrate its solution using either the substitution or elimination method.

Click Start a New Conversation and make the problem number and topic (#10 Jarod and the Bunnies) the subject of your post.

The answers are at the end of the file, so don’t just give an answer—we
can already see what the answers are. Don’t post an explanation unless
your answer matches the correct one!

This is a moderated forum. Your posting will not be visible to the rest
of the class until I approve it. Occasionally, more than one person
will tackle a problem before they can see the work of others. In that
case, credit will be given to all posters. Once the solution to a
problem has become visible, that problem is off limits and you will need
to choose a different problem in order to get credit.

I will indicate in the grading comments if corrections need to be made.
If you haven’t received credit, first double-check for my comments in
the gradebook. If everything looks OK, then Message me asking me to
check on it.

You must make the necessary corrections and have your work posted in order to receive credit.

Your initial post is worth 10 points. It is not necessary to respond to
2 classmates on this forum, although a request for clarification on the
procedure used would be appropriate. Also, I’m sure that a “Thank You”
for an exceptionally clear explanation would be welcome!
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Forum: If
Only I Had a System…

Applications
of Systems of Linear Equalities
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The
Problem:
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When students are surveyed about what makes a
good math Forum, at least half of the responses involve

·
“discussing
how to work problems”
·
“seeing how this math
applies to real-life situations”

This
Forum on applications of systems of
equations addresses both of these concerns.

Unfortunately,
the typical postings are far from ideal.

This
is an attempt to rectify the situation. Please read
this in its entirety before you post
your answer!
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Pick-up
games in the park vs. the NBA:

Shooting
hoops in the park may be lots of fun, but it scarcely qualifies as the
precision play of a well-coached team. On the one hand, you have individuals
with different approaches and different skill levels, “doing their own
thing” within the general rules of the game. On the other hand you have
trained individuals, using proven strategies and basing their moves on
fundamentals that have been practiced until they are second nature.

The
purpose of learning algebra is to change a natural, undisciplined approach to
individual problem solving into an organized, well-rehearsed system that will
work on many different problems. Just like early morning practice, this might
not always be pleasant; just like Michael Jordan, if you put in the time
learning how to do it correctly, you will score big-time in the end.
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.gif”>.gif”>.gif”>.jpg”>But my brain just doesn’t
work that way. . .
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Nonsense!
This has nothing to do with how your brain works. This is a matter of learning
to read carefully, to extract data from the given situation and to apply a
mathematical system to the data in order to obtain a desired answer. Anyone can
learn to do this. It is just a matter of following the system; much like making
cookies is a matter of following a recipe.
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“Pick-up
Game” Math
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It is appalling how many responses involve plugging in
numbers until it works.

·
“My birthday is the eleventh, so I
always start with 11 and work from there.”

·
“The story involved both
cats and dogs so I took one of the numbers, divided by 2 and then I
experimented.”
·
“First I fire up
Excel…”

·
“I know in real-life
that hot dogs cost more than Coke, so I crossed my fingers and started with
$0.50 for the Coke…”

The
reason these “problem-solving” boards are moderated is so that these
creative souls don’t get everyone else confused!
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NBA Math

In
more involved problems, where the answer might come out to be something
irrational, like the square root of three, you are not likely to just randomly
guess the correct answer to plug it in. To find that kind of answer by an
iterative process (plugging and adjusting; plugging and adjusting; …) would
take lots of tedious work or a computer. Algebra gives you a relative
painless way of achieving your objective without wearing your pencil to the
nub.

The
reason that all of the homework has involved x’s and y’s and two equations, is
that we are going to solve these problems that way. Each of these problems is a
story about two things, so every one of these is going to have an x and a y.

In
some problems, it’s helpful to use different letters, to help keep straight
what the variables stand for. For example, let L = the length of the rectangle
and W = the width.

The biggest advantage to this method is that
when you have found that w = 3 you are more likely to notice that you still
haven’t answered the question, “What is the length of the rectangle?”

Here are
the steps to the solution process:

·
Figure out from the story what those two things are.o
one of these will be x

o the other
will be y

·
The first sentence of your
solution will be “Let x = ” (or “Let L = ” )

o Unless
it is your express purpose to drive your instructor right over the edge, make sure
that your very first word is “Let”

·
The second sentence of your
solution will be “Let y = ” (or “Let W = ” )

·
Each story gives two different relationships
between the two things.

o
Use one of those relationships to
write your first equation.

o
Use the second relationship to
write the second equation.

·
Now demonstrate how to solve
the system of two equations. You will be using either

o
substitution

o orelimination- just
like in the homework.
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.jpg”>More examples…
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For this problem, I’d
use substitution to solve the system of
equations:

The length of a rectangle blah, blah, blah…

Let L = the length
of the rectangle

… blah, blah,
blah twice the width

Let W = the width
of the rectangle

The
length is6 inches less than twice the width

L = 2W

– 6

The
perimeter of the rectangle is56

2L + 2W

=56

For this one, I’d use
elimination to solve the system of
equations:

Blah, blah, blah
bought 2 cokes…

Let x = the price of a
coke

.. blah, blah, blah
4 hot dogs

Let y = the price of a
hot dog

2 cokes plus 4 hot
dogs cost 8.00

2x + 4y = 8.00

3 cokes plus 2 hot
dogs cost 8.00

3x + 2y = 8.00

For this
one, I’d use substitution to solve the
system of equations:

One
numberis
blah, blah, blah…

Let x = the first number

…blah,
blah, blah triplethe second number

Let y = the second
number

The
first number istriple the second

x = 3y

The sum
of the numbers is24

x + y = 24

.jpg”>Checking your answers vs. Solving the problem
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The
problem:
Two numbers add to give 4 and subtract to give 2. Find the numbers.

Solving
the problem:

Let
x = the first number Let y = the second number

Two
numbers add to give 4: x + y = 4 Two numbers subtract to give 2: x – y = 2

Our two equations
are: x + y = 4

x – y = 2 Adding the equations we get 2x = 6

x
= 3 The first
number is 3.

x
+ y = 4 Substituting that answer into equation 1 3 + y = 4

y = 1 The second
number is 1.

Checking the answers:

Two numbers add to
give 4:

3
+ 1 = 4

The two numbers
subtract to give 2:

3 – 1 = 2

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Do
NOT demonstrate how to check the answers
that are provided and call that demonstrating how to solve the problem!
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Formulas
vs. Solving equations
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Formulas
express standard relationships between measurements of things in the real world
and are probably the mathematical tools that are used most frequently in real
-life situations.

Solving equations involves getting an answer
to a specific problem, sometimes based on real-world data, and sometimes not.
In the process of solving a problem, you may need to apply a formula. As a
member of modern society, it is assumed that you know certain common formulas
such as the area of a square or the perimeter of a rectangle. If you are unsure
about a formula, just Google it. Chances are excellent it will be in one of the
first few hits.

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If
you are still baffled:
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·
Watch a lecture
on “Applications of Systems of Equations”

·
Watch this video:

Solve applications of systems of linear equations or inequalities

·
View the PowerPoint Presentations that are provided in the
link from the Lesson section.

·
Message meif you are
still confused.

Systems of Equations

1) A vendor sells hot dogs and bags
of potato chips. A customer buys 4 hot

1)

dogs and 5 bags of potato chips for
$12.00. Another customer buys 3 hot

dogs and 4 bags of potato chips for
$9.25. Find the cost of each item.

2) University Theater sold 556
tickets for a play. Tickets cost $22 per adult

2)

and $12 per senior citizen. If
total receipts were $8492, how many senior

citizen tickets were sold?

3) A tour group split into two
groups when waiting in line for food at a fast

3)

food counter. The first group
bought 8 slices of pizza and 4 soft drinks

for $36.12. The second group bought
6 slices of pizza and 6 soft drinks

for $31.74. How much does one slice
of pizza cost?

4) Tina Thompson scored 34 points
in a recent basketball game without

4)

making any 3-point shots. She scored 23 times,
making several free

throws worth 1 point each and
several field goals worth two points each.

How many free throws did she make?
How many 2-point field goals

did she make?

5) Julio has found that his new car
gets 36 miles per gallon on the highway

5)

and 31 miles per gallon in the
city. He recently drove 397 miles on 12

gallons of gasoline. How many miles
did he drive on the highway? How

many miles did he drive in the
city?

6) A textile company has specific
dyeing and drying times for its different

6)

cloths. A roll of Cloth A requires
65 minutes of dyeing time and 50

minutes of drying time. A roll of
Cloth B requires 55 minutes of dyeing

time and 30 minutes of drying time.
The production division allocates

2440 minutes of dyeing time and
1680 minutes of drying time for the

week. How many rolls of each cloth
can be dyed and dried?

7) A bank teller has 54 $5 and $20
bills in her cash drawer. The value of the

7)

bills is $780. How many $5 bills
are there?

8) Jamil always throws loose change
into a pencil holder on his desk and

8)

takes it out every two weeks. This
time it is all nickels and dimes. There

are 2 times as many dimes as
nickels, and the value of the dimes is $1.65

more than the value of the nickels.
How many nickels and dimes does

Jamil have?

9) A flat rectangular piece of
aluminum has a perimeter of 60 inches. The

9)

length is 14 inches longer than the
width. Find the width.

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1

10) Jarod is having a problem with
rabbits getting into his vegetable garden,

10)

so he decides to fence it in. The
length of the garden is 8 feet more than 3

times the width. He needs 64 feet
of fencing to do the job. Find the

length and width of the garden.

11) Two angles are supplementary if
the sum of their measures is 180°. The

11)

measure of the first angle is 18°
less than two times the second angle.

Find the measure of each angle.

12) The three angles in a triangle
always add up to 180°. If one angle in a

12)

triangle is 72° and the second is 2
times the third, what are the three

angles?

13) An isosceles triangle is one in
which two of the sides are congruent. The

13)

perimeter of an isosceles triangle
is 21 mm. If the length of the

congruent sides is 3 times the
length of the third side, find the

dimensions of the triangle.

14) A chemist needs 130 milliliters
of a 57% solution but has only 33% and

14)

85% solutions available. Find how
many milliliters of each that should

be mixed to get the desired
solution.

15) Two lines that are not parallel
are shown. Suppose that the measure of angle 1

15)

is (3x+ 2y)°, the measure of angle 2 is
9y°, and the measure of angle 3 is (x+ y)°.

Find x and y.

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A)
x=

324,
y= 36

B)
x=

36,
y= 324

7

7

7

7

C)
x=

36 , y=

288

D)
x=

288 , y=

36

7

7

7

7

16) The manager of a bulk foods establishment
sells a trail mix for $8 per

16)

pound and premium cashews for $15
per pound. The manager wishes to

make a 35-pound trail mix-cashew mixture that will sell for
$14 per

pound. How many pounds of each
should be used?

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2

17)
Kelly is a partner in an Internet-based seed and garden supply
business. 17) The company offers a blend of exotic wildflower seeds for $95 per

pound and a blend of common
wildflower seeds for $30 per pound. Kelly is creating a medium-price product by mixing together 33
pounds of the more expensive blend with 6 pounds of the less expensive blend.
What will be the price per pound for the new blend? (Round to the nearest cent,
if necessary.)
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18) A college student earned $7300
during summer vacation working as a

18)

waiter in a popular restaurant. The
student invested part of the money at

7% and the rest at 6%. If the
student received a total of $458 in interest at

the end of the year, how much was
invested at 7%?

19) A retired couple has $160,000
to invest to obtain annual income. They

19)

want some of it invested in safe
Certificates of Deposit yielding 6%. The

rest they want to invest in AA
bonds yielding 11% per year. How much

should they invest in each to realize
exactly $15,600 per year?

20) A certain aircraft can fly 1330
miles with the wind in 5 hours and travel

20)

the same distance against the wind
in 7 hours. What is the speed of the

wind?

21) Julie and Eric row their boat
(at a constant speed) 40 miles downstream

21)

for 4 hours, helped by the current.
Rowing at the same rate, the trip back

against the current takes 10 hours.
Find the rate of the current.

22) Khang and Hector live 88 miles
apart in southeastern Missouri. They

22)

decide to bicycle towards each
other and meet somewhere in between.

Hector?s rate of speed is 60% of
Khang?s. They start out at the same time

and meet 5 hours later. Find
Hector?s rate of speed.

23) Devon purchased tickets to an
air show for 9 adults and 2 children. The

23)

total cost was $252. The cost of a
child?s ticket was $6 less than the cost of

an adult?s ticket. Find the price
of an adult?s ticket and a child?s ticket.

24) On a buying trip in Los
Angeles, Rosaria Perez ordered 120 pieces of

24)

jewelry: a number of bracelets at
$8 each and a number of necklaces at

$11 each. She wrote a check for
$1140 to pay for the order. How many

bracelets and how many necklaces
did Rosaria purchase?

25) Natasha rides her bike (at a
constant speed) for 4 hours, helped by a

25)

wind of 3 miles per hour. Pedaling
at the same rate, the trip back against

the wind takes 10 hours. Find find
the total round trip distance she

traveled.

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3

26) A barge takes 4 hours to move
(at a constant rate) downstream for 40

26)

miles, helped by a current of 3
miles per hour. If the barge?s engines are

set at the same pace, find the time
of its return trip against the current.

27) Doreen and Irena plan to leave
their houses at the same time, roller

27)

blade towards each other, and meet
for lunch after 2 hours on the road.

Doreen can maintain a speed of 2
miles per hour, which is 40% of Irena?s

speed. If they meet exactly as
planned, what is the distance between

their houses?

28) Dmitri needs 7 liters of a 36%
solution of sulfuric acid for a research

28)

project in molecular biology. He
has two supplies of sulfuric acid

solution: one is an unlimited
supply of the 56% solution and the other

an unlimited supply of the 21%
solution. How many liters of each

solution should Dmitri use?

29) Chandra has 2 liters of a 30%
solution of sodium hydroxide in a

29)

container. What is the amount and
concentration of sodium hydroxide

solution she must add to this in
order to end up with 6 liters of 46%

solution?

30) Jimmy is a partner in an
Internet-based coffee supplier. The company

30)

offers gourmet coffee beans for $12
per pound and regular coffee beans

for $6 per pound. Jimmy is creating
a medium-price product that will

sell for $8 per pound. The first
thing to go into the mixing bin was 10

pounds of the gourmet beans. How
many pounds of the less expensive

regular beans should be added?

31) During the 1998-1999 Little League season, the
Tigers played 57 games.

31)

They lost 21 more games than they
won. How many games did they win

that season?

32) The perimeter of a rectangle is
48 m. If the width were doubled and the

32)

length were increased by 24 m, the
perimeter would be 112 m. What are

the length and width of the
rectangle?

33) The perimeter of a triangle is
46 cm. The triangle is isosceles now, but if

33)

its base were lengthened by 4 cm
and each leg were shortened by 7 cm, it

would be equilateral. Find the
length of the base of the original triangle.

34) The side of an equilateral
triangle is 8 inches shorter than the side of a

34)

square. The perimeter of the square
is 46 inches more than the perimeter

of the triangle. Find the length of
a side of the square.

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4

35) The side of an equilateral
triangle is 2 inches shorter than the side of a

35)

.jpg”>square. The perimeter of the square
is 30 inches more than the perimeter of the triangle. Find the length of a side
of the triangle.

5

Answer Key
Testname: SYSTEMS_OF_EQUATIONS

1) $1.75 for a hot dog; $1.00 for a bag
of potato chips
2) 374 senior citizen tickets
3) $3.74 per slice of pizza
4) 12 free throws, 11 field goals
5) 180 miles on the highway, 217 miles
in the city
6) 24 rolls of Cloth A, 16 rolls of
Cloth B
7) 20 $5 bills
8) 11 nickels and 22 dimes
9) 8 inches
10) length: 26 feet; width: 6 feet
11) first angle= 114° second angle= 66°

12) 72°, 72°, 36°
13) 3 mm, 9 mm, 9 mm
14) 70 mL of 33%; 60 mL of 85%

15) D

16) 5 pounds of trail mix
30 pounds of cashews
17) $85.00 per pound
18) $2000
19) $120,000 at 11% and $40,000 at 6%
20) 38 mph
21) 3 mph
22) 6.6 mph
23) adult?s ticket: $24; child?s ticket:
$18
24) 60 bracelets and 60 necklaces
25) 80 mi
26) 10 hr
27) 14 mi
28) 56% solution: 3 L; 21% solution: 4 L
29) 4 L of 54% solution
30) 20 lb
31) 18 games
32) Length: 16 m; width: 8 m
33) 8 cm
34) 22 inches
35) 22 inches

6