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07 April 2009 @ 09:38 am
Need math help - word problems  

I'm looking for someone who is good with math.  I am not good with matrices or word problems and these four problems on my homework are kiling me.  If someone could show me how to do any of these, it would be appreciated.

 

Five neighborhoods (NB) all want to raise money for a playground for their kids. The neighborhood that raises the most money will be able to choose the name of the park. To raise money, they all decide to have a bake sale and sell cookies (C), cakes (K), and muffins (M). They plan to sell their bake goods on Saturday morning for 3 weeks. Following are the results of the first 2 weeks. The numbers represent the number of cookies, cakes, and muffins sold.

 

 

 

 A. How much of each item had the neighborhoods sold by the end of the second week? Use matrices to solve the problem. Final answer must be given in matrix form. Show all   work to receive full credit.

 

 

B. Which team sold the most items at the end of the second week?

 

 

D. How much money did the neighborhoods make for their playground?

 

E. Which neighborhood gets to name the park?

 

 

 

2. Use augmented matrices to solve the following 2x2 systems of equations.  Show all work for full credit.  Final answer must be given in matrix form.
 -5x+7=9
x+10y=21

x+5y=11
2x+10y=25

A group of students decides to sell pizzas to help raise money for their senior class trip. They sold pepperoni for $12, sausage for $10, and cheese for $8. At the end of their sales the class sold a total of 600 pizzas and made $5900. The students sold 175 more cheese pizzas than sausage pizzas. Set up a system of three equations and three unknowns, use an augmented matrix to solve, and show all work to receive full credit.

 

A. What are the three unknowns?

           

B. Write a separate equation representing each of the first three sentences.

 

C. Determine the augmented matrix that represents the three equations.

 

D. Solve for the matrix. Show all work to receive full credit.

  

 

E. How many of each type of pizza were sold?



A company’s employees are working to create a new energy bar. They would like the two key ingredients to be peanut butter and oats, and they want to make sure they have enough carbohydrates and protein in the bar to supply the athlete. They want a total of 31 carbohydrates and 23 grams of protein to make the bar sufficient. Using the following table, create a system of two equations and two unknowns to find how many tablespoons of each ingredient the bar will need. Solve the system of equations using matrices. Show all work to receive full credit.


 

A. Write an equation for the total amount of carbohydrates.

 

 

 

B. Write an equation for the total amount of protein.  

 

 

 

 

C. Determine the augmented matrix that represents the equations from A and B.

 

 

 

 

D. Solve for the matrix above. Show all work to receive full credit.

 

 

E. How many tablespoons of each will there need to be for the new energy bar?

 

C. By the end of the third week, the totals were as follows:



If the neighborhoods makes a $0.50 profit on each cookie, a $5.00 profit on each cake, and a $1.00 profit for each muffin they sell, how much profit did each neighborhood make? Final answer must be given in matrix form. Show all work to receive full credit.

 

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I feel: curiouscurious
I'm listening to: Cooling by Tori Amos
 
 
 
cecily1880cecily1880 on April 7th, 2009 02:53 pm (UTC)
Yes, I probably can - tell me a quick overview of how far you are in your studies. You know about Matrix multiplication, or at least how to multiply a matrix by a vector?

whoops - have to go, boos around talk later...
Lady Manson: spn - dean jess its aliveladymanson on April 7th, 2009 02:59 pm (UTC)
Oh, you're so sweet for offering to help - thank you! I'm having the hardest time with this class! As of right now,

I know pretty much nothing about matrices. I haven't done them since high school, which was nearly 10 years ago.

Also, I love that you ducked out when your boss came by. I'm the same way. :-)

Thanks again for any help you can provide!
cecily1880cecily1880 on April 7th, 2009 09:40 pm (UTC)
Right, well we seem to be in complete agreement, except I haven't done matrices for 20 years. However, the advantage of maths is ,unlike physics, it's mostly immutable. 2+2 still makes 4, even 20 years later.

sooo,

A. How much of each item had the neighborhoods sold by the end of the second week? Use matrices to solve the problem. Final answer must be given in matrix form. Show all work to receive full credit.
That will be A+B (your working, ie minimal!)
The numerical values will be
Each cell in A add to the same cell in B.
so the first cell is NB#1 Cookies in week 1, (A1,1) ie 20 plus NB#1 C in week 2 (B1,1) ie 10 = 30
I am using A1,1 instead of the subscripts, because I'm using crappy text, not rich text etc. Maths is hard with just a typewriting script! So, the notation is A3,2 is 5.

and I was trying to cut and paste the figures and realise you have a picture of the numbers, so anyhow, just add them up.

Then you get matrix X (say) which is A+B=X

We use X for the rest of the question (so feel free to post your answer here so I can check it because all your answers will be based on it, so it needs to be right.)

B. Which team sold the most items at the end of the second week?
Working:
Add up the rows ie NB#3 formula is X3,1 + X3,2 + X3,3
ie since X=A+B, this is the same as (A3,1+B3,1) + (A3,2+B3,2) + (A3,3+B3,3)

So NB#4 has sold 60+5+28 items

C. You can use matrix multiplication by a vector for this if you have already been taught this.

Use the vector v=($0.5 $5 $1) and multiply X.v
ie for NB#4, the row in X is (60 5 28), so (60*$0.5 +5*$5 +28*$1) = $83 (but check my arithmetic, always.)

Do this for all NB#s and see who won.

Question 2 I think you have a typo, btw, there should be a y I am sure.
-5x+7y=9
x+10y=21

Augmented matrix. is ( -5 7 9)
(1 10 21)

You must perform only elementary transformations (in case you are not sure of the definition here it is)
http://en.wikipedia.org/wiki/Elementary_matrix_transformations

to end up with a matrix that is (1 0 x)
(0 1 y)
soooo
I'd multiply row 2 by 5
(5 50 105)
then add up both rows and replace row 2 with that, giving
(0 57 114)
The divide by 57
so row 2 is (0 1 2)
Then subtract 7x row 2 from row 1
(-5 0 9-14) = (-5 0 -5) and divide by -5 giving (1 0 1)
so the final matrix is
(1 0 1)
(0 1 2)
so the equations are:
x=1
y=2

Repeat for second set..... ;-)


A group of students decides to sell pizzas to help raise money for their senior class trip. They sold pepperoni for $12, sausage for $10, and cheese for $8. At the end of their sales the class sold a total of 600 pizzas and made $5900. The students sold 175 more cheese pizzas than sausage pizzas. Set up a system of three equations and three unknowns, use an augmented matrix to solve, and show all work to receive full credit.


cecily1880cecily1880 on April 7th, 2009 09:48 pm (UTC)
unknowns are # of each pizza, p=pepper, s=sausage, c=cheese.

They sold 600 pizzas so p+s+c=600
they made 5900 so 12p+10s+8c=5900
AND c=s+175, so c-s=175, which is in this format 0p-s+c=175


Those are my three equations.

matrix
(1 1 1 600 )
(12 10 8 5900)
(0 -1 1 175 )
Do the same, I'd recommend use row 3 because that's nice, add to row 1.
then and multiply by 10, add to row 2, and continue to manipulate, adding and multiplying, until you get
(1 0 0 p)
(0 1 0 s)
(0 0 1 c)

Hopefully that helps, and you can carry on with the next one.
Lady Manson: spn - dean b&wladymanson on April 8th, 2009 08:55 pm (UTC)
THANKS SO MUCH!!!!
You are extremely helpful - I REALLY appreciate it. Hopefully this will turn out well. Thanks again! :-)
mutu26 on September 8th, 2010 02:04 pm (UTC)
I have quite big experience with word documents. And some times I had like issues and lately I found out the solution in my view, which solved my problem several days ago, and maybe it can help in such condition - word recover.