This Blog exists for the collective benefit of all algebra students. While the posts are specific to Mr. Chamberlain's class, any and all "algebra-ticians" are welcome. The more specific your question (including your own attempts to answer it) the better.
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Thursday, February 24, 2011
hw #6-7 Systems of Equations and Inequalities Review
Complete ProbSet 6R
pg 399 #22,23,25
optional homework (only for students that want to do well on tests)
pg 404-407 1-infinity including Chapter Test
On number 4 in problem set 6R I was having trouble where to begin. I was able to explicitly define the variables but I was having trouble with the equations. I was able to get the correct answer (48), but not algebraically. It just came to me when I read the problem.
Overrall, I don't really understand how you can combine pounds to make a pound cost that is less that the other.. Would this be right? For #3? c= # of lbs of cashew nuts p= # of lbs of peanuts
How many pounds of cashew nuts that sell for $2 pound should be mixed with peanuts, which sell for 80¢ a pound, to make a 10-pound mixture that sells for $1.28 a pound?
I'm going to ask your 5th grade sibling a question: If a mixture sells for $1.28/lb, how much will 10 lbs cost?
When they give you the answer, then tell me why all of your 10 lb mixtures are adding up to only $1.28... thanks!
Also, I didn't understand how in class we came up with the equation 4(x-y)=1560.. I think that problem (#2) is somewhat similar to #7, and I can't seem to figure out how to get the equations.
An art museum has a general admission rate of $5, but students pay $3. Yesterday, the museum collected a total of $902 from 216 people. How many general admission customers attended the museum?
hopefully you defined your variables as: x (or 'g') is the number of general admission tix y (or 's')is the number of student tix
For the airplane/wind and boat/current problems, you are sometimes asked to find the speed of the object (plane/boat) separate from the force (wind/current).
I think you know that if you travel at 60mph for 4 hours, you would travel 4(60) miles, or 240 miles, right?
If you are traveling in an object at an unknown speed, x, and are traveling against the unknown force speed, y, then the overall average speed will be (x-y), right? If you travel for 4 hours at that speed, you would travel a total of 4(x-y) miles, right? If you are then told that you traveled a total of 1,560 miles, you could then set up an equation... 4(x-y)=1560... right?
Okay, gotcha on the digits one, but I still don't understand what the force speed & the speed are & why you would have to subtract them from eachother?
For the sake of the object/force problems... if the plane has a "still" air speed of 600mph, the means that the plane will travel at 600mph is there is no wind (i.e. still air). If there is a headwind (wind is against) the speed of the plane will be the still-air speed MINUS the wind-speed... if there is a tailwind (wind behind or with) the speed of the plane will be calculated as the still air speed PLUS the speed of the wind.
I don't know if I did this right.. on the last page of the Problem Set, I was doing 1) for the solving equations, and I got a really wierd decimal from substituting..
Why don't you share the particular question and your answer, and let's see if any of your peers can check in and validate. Does your graph validate your algebraic answer?
If we are unorganized and we are going to start keeping an organized binder as of Monday, what should we do for the notebook quiz? Should we just tell you we are starting over. ????
Yes, inequalities in the coordinate plane are similar to equations. In both cases, you have to graph lines, and the same techniques, (slope-intercept or thumb cover-up) work for both. With inequalities, you have the extra burden of test points to determine where the shading goes.
It takes a carpenter 6 hours and 20 minutes to make 4 small cabinets and 4 large cabinets. It takes her 4 hours and 5 minutes to make 2 small cabinets and 3 large cabinets. How long does it take her to make one small cabinet?
At a local health club, members pay a $35 membership fee and $1.50 for each spinning class. Non-members pay $5 for each spinning class. After how many spinning classes will the cost be the same for a member and a non-member?
If the ratio of novelists to poets is 5 to 3, then that also means that the ratio of novelists to the total number of writers in the workshop is 5 out of 8, yes?
What don't you know. How many liters of each solution will blend to make the 42% solution.
x is the liters of 30% solution y is the liters of 50% solution
.30x + .50y = .42(200) x + y = 200
The first equation means that x liters of the 30% solution when combined with y liters of the 50% solution will be equal to 200 liters of the 42% solution.
re-write as: .30x + .50y = 84 x + y = 200
and weeeeeee... the alg rollercoaster takes you to:
80 liters of the 30% solution 120 liters of the 50% solution
I was kind of confused on #3 in problem set 6R. I ended up with negative something cashews or peanuts (not sure which one). Please Help.
ReplyDeleteOn number 4 in problem set 6R I was having trouble where to begin. I was able to explicitly define the variables but I was having trouble with the equations. I was able to get the correct answer (48), but not algebraically. It just came to me when I read the problem.
ReplyDeleteSame here. On paper the math works out, but when I actually do the calculations it comes out to something like -15 pounds of peanuts.
ReplyDeleteI know right. I hate when that happens. You do all the work and you have the right answer but your calculations tell you that you're wrong.
ReplyDeleteHow do you get the equation for #3 in Problem Set 6R, the one where they add up to 1.28 a pound? I don't understand..
ReplyDeleteI have the same problem with #4 as Anonymous up there.. I can explicitly state the variables but I don't know where to start..
ReplyDeleteOverrall, I don't really understand how you can combine pounds to make a pound cost that is less that the other.. Would this be right? For #3?
ReplyDeletec= # of lbs of cashew nuts
p= # of lbs of peanuts
2c+80p=1.28
??
Do you just add them together like that?
ReplyDelete"2c+.80p-1.28"
?
For #6, do you just have to figure out what "y=" if your y= # of general admissions?
ReplyDeleteSo here is the NUTTY question:
ReplyDeleteHow many pounds of cashew nuts that sell for $2 pound should be mixed with peanuts, which sell for 80¢ a pound, to make a 10-pound mixture that sells for $1.28 a pound?
I'm going to ask your 5th grade sibling a question:
If a mixture sells for $1.28/lb, how much will 10 lbs cost?
When they give you the answer, then tell me why all of your 10 lb mixtures are adding up to only $1.28... thanks!
Ca-peesh??
For #4, if x is the tens digit and y is the singles digit... you need to know that the VALUE of the tens digit is actually 10x, right??
ReplyDeletelmk if that helps...
Also, I didn't understand how in class we came up with the equation 4(x-y)=1560.. I think that problem (#2) is somewhat similar to #7, and I can't seem to figure out how to get the equations.
ReplyDeleteHere is question #6 from ProbSet 6R:
ReplyDeleteAn art museum has a general admission rate of $5, but students pay $3. Yesterday, the museum collected a total of $902 from 216 people. How many general admission customers attended the museum?
hopefully you defined your variables as:
x (or 'g') is the number of general admission tix
y (or 's')is the number of student tix
From there, I don't understand your question.
So should I multiply $1.28 for the nuts one?
ReplyDeleteOohhh I understand.. For #4.. Let me try to work on it..
ReplyDeleteAnd for the nuts one, what I meant is multiply it by then and then put it into the equation? 2c+.80p=12.80
?
For the digits problem, I came up with one equation; x+y=12. I can't seem to find the other equation? Would it be 10x+y=12x
ReplyDelete??
For the airplane/wind and boat/current problems, you are sometimes asked to find the speed of the object (plane/boat) separate from the force (wind/current).
ReplyDeleteI think you know that if you travel at 60mph for 4 hours, you would travel 4(60) miles, or 240 miles, right?
If you are traveling in an object at an unknown speed, x, and are traveling against the unknown force speed, y, then the overall average speed will be (x-y), right? If you travel for 4 hours at that speed, you would travel a total of 4(x-y) miles, right? If you are then told that you traveled a total of 1,560 miles, you could then set up an equation... 4(x-y)=1560... right?
Ca-peesh?
Dear Digits,
ReplyDeleteWhy don't you treat it like a system of equations, solve it and see what it tells you???????
Mr. C.
Okay, gotcha on the digits one, but I still don't understand what the force speed & the speed are & why you would have to subtract them from eachother?
ReplyDeleteOkay, I figured out #4!
ReplyDeleteFor the sake of the object/force problems... if the plane has a "still" air speed of 600mph, the means that the plane will travel at 600mph is there is no wind (i.e. still air). If there is a headwind (wind is against) the speed of the plane will be the still-air speed MINUS the wind-speed... if there is a tailwind (wind behind or with) the speed of the plane will be calculated as the still air speed PLUS the speed of the wind.
ReplyDeleteCa-peesh?
OHHHH I understand now!
ReplyDeleteI don't know if I did this right.. on the last page of the Problem Set, I was doing 1) for the solving equations, and I got a really wierd decimal from substituting..
ReplyDeleteWhy don't you share the particular question and your answer, and let's see if any of your peers can check in and validate. Does your graph validate your algebraic answer?
ReplyDeleteFor #10 on pg 405, how should I start? I don't know how to get started & board the rollercoaster.
ReplyDeleteDo you have to define variables for Jenna & Jay or for the # of years?
ReplyDeleteIf we are unorganized and we are going to start keeping an organized binder as of Monday, what should we do for the notebook quiz? Should we just tell you we are starting over. ????
ReplyDeletei think i get it...
ReplyDeletei was wondering about solving and graphing systems of inequalities but i get it now...
i looked back in the book and my dad helped me...you have to treat it like the cover-up method...
i think...someone tell me if i am wrong!
Dear #10,
ReplyDeleteWhat don't you know... the number of years, right?
Set up a variable
x is the number of years from NOW
y is the number of songs written
Can you write an equation for Jay? for Jenna?
When will 'y' be the same number for both equations?
give it a try and lmk
Dear Unorganized,
ReplyDeleteI suffer from the same "malady." If you are willing to admit you need help... I am willing to give you a clean slate.
Let's work on it together!
Hey Justin,
ReplyDeleteYes, inequalities in the coordinate plane are similar to equations. In both cases, you have to graph lines, and the same techniques, (slope-intercept or thumb cover-up) work for both. With inequalities, you have the extra burden of test points to determine where the shading goes.
Would the equations for #10 be y=24+6x & y=12x ?
ReplyDeleteI don't know how to make equations for #18.. First they talk about haircuts, then they talk about cost!!
ReplyDeleteIt takes a carpenter 6 hours and 20 minutes to make 4 small cabinets and 4 large cabinets. It takes her 4 hours and 5 minutes to make 2 small cabinets and 3 large cabinets. How long does it take her to make one small cabinet?
ReplyDeleteSet up a system of equations and solve:
ReplyDeleteAt a local health club, members pay a $35 membership fee and $1.50 for each spinning class. Non-members pay $5 for each spinning class. After how many spinning classes will the cost be the same for a member and a non-member?
x=Membership fee
ReplyDeletey=Non-Members' fee
z= # of spinning classes taken
x=35+1.5z
y=5z
Is it correct? Are there supposed to be 3 variables?
Will the test have any questions involving ratios like #14 ? If yes, please explain how to do these. D:
ReplyDeleteYou KNOW the fees:
ReplyDeletex is the number of spinning classes
y is the total cost charged
You were kinda close, but you don't need separate variables for the total cost
y=1.50x+35
y=5x
(I mean #14 on the Chapter Test)
ReplyDeleteOk I got it!
ReplyDeleteI also need help with #18.. How do you make the equations?
ReplyDeleteFor this test. I'm not crazy about #14 on the Chapter Test (pg 407). Wouldn't we use a proportion to solve that one?
ReplyDeleteIn other words, you should be comfortable solving it (using a proportion)... a system of equations seems like needless extra work to me.
5/8 = x/24
and that's all... do you agree?
Where did you get the 8 from? Or did you mean 3?
ReplyDelete& I still can't figure out how to do #7..
ReplyDelete#18 on page 405... that's a good problem.
ReplyDeleteWhat don't you know? How much the owner charges (x) and how much the asst charges (y), right?
x is the amount the owner charges per hc
y is the amount the asst charges per hc
6x + 12y = 750
x = y + 20
Looks like a perfect job for SUBSTITUTION to me, yes?
6(y+20) + 12y = 750... weeeeeeeeeeeeeeeeee!!!!
6y+120+12y=750
18y+120=750
18y=630
y=630/18
y=35
since x=y+20
The owner charges $55 per hc, yes?
P.S. I will not be getting my hair cut by either one of those two!!
Oops sorry I meant 15 :O
ReplyDeleteIf the ratio of novelists to poets is 5 to 3, then that also means that the ratio of novelists to the total number of writers in the workshop is 5 out of 8, yes?
ReplyDeleteNevermind about that comment up there ^^
ReplyDeleteI also need help w/ 15 on Chap. Test
Which #7?
ReplyDeleteOhhhh (For the novelists) I get it.. Because you add them together to make the total amount of participants. Got it.
ReplyDeleteOh, in the Problem Set 6R.. With the currents...
ReplyDelete#7
& Thanks for the help on #18!!
ReplyDeleteAhhh, another mixture problem (#15)
ReplyDeleteWhat don't you know. How many liters of each solution will blend to make the 42% solution.
x is the liters of 30% solution
y is the liters of 50% solution
.30x + .50y = .42(200)
x + y = 200
The first equation means that x liters of the 30% solution when combined with y liters of the 50% solution will be equal to 200 liters of the 42% solution.
re-write as:
.30x + .50y = 84
x + y = 200
and weeeeeee... the alg rollercoaster takes you to:
80 liters of the 30% solution
120 liters of the 50% solution
The currents are treated the same as the wind. Still air speed and still water speed... same concepts. Can you try to set it up?
ReplyDeleteOkay Thanks ! :)
ReplyDeleteI gotta remember that last multiplication step.. with the * 200 L!
I can try.. Hold on a second..
ReplyDeleteWould it be??
ReplyDeletex-y=60(6)
y=60(5)
x is the still water speed of the boat (mph)
ReplyDeletey is the speed of the current (mph)
The speed in mph when with the current is (x+y)
The speed in mph against the current is (x-y)
Distance = rate*time, right
so,
Time*rate=distance, yes?
5(x+y)=60
6(x-y)=60
yes??
i have no idea what im doing
ReplyDeleteYay! Someone new! :)
ReplyDeleteAnd hold on I have to read your answer..
Oohhh I gotsk it.. Gotta remember that, too..
ReplyDeleteThat's all my questions :) I'll try to review a bit more in the morning :) Thanks for the help, Mr.C! :)
ReplyDeleteWait-- Could the still water speed of the boat be -1 mph? hahahah That was my answer When I substituted!
ReplyDeleteFor 6R #7, if you solve:
ReplyDelete5(x+y)=60
6(x-y)=60
you'll get
x=11
y=1
The speed of the boat in still water is 11mph
The speed of the current is 1 mph
yes?
Yes!
ReplyDelete