Confusing essay question system of equations + inverse matri

[ginamv]

My teacher for Algebra II gave us this essay question and said we could get help from anyone or any source so I came here for help! Here is the question:

Cajun Joe makes a gumbo that uses sausage, rice, and vegetables. The sausage costs $3 a pound, the rice costs $1.50 a pound, and the vegetables cost $0.75 a pound. Joe makes batches of gumbo that use a total of 20 pounds of ingredients and costs $1.50 per pound. Joe uses the same weight of rice as he does vegetables.

a. Write a system of equations to using x as the number of pounds of sausage used, y as the number of pounds of rice used, and z as the number of pounds of vegetables used. Then write a matrix equation to solve the system.

b. Use an inverse matrix to solve the system

c. Joe also makes a "meaty" version of his gumbo that uses the same amount of sausage as rice in each 20 pound batch and costs $1.65 a pound. Write a system of equations for the "meaty" version of Joe's gumbo. The use an inverse matrix to solve the system. Explain why the "meaty" version costs more per pound.


That sure seems like a big question to me and I'm not sure where to start and most certainly not sure how to finish. My teacher goes over 3 lessons per day in our book and moves very fast. My mom is going to get me a tutor this week, but I would appreciate any help that anyone can give on this question. I have 8 total questions in all and this is just the first one!

Thank you to anyone that can help me.

-G

 

[stapel]

I'm not sure where to start and most certainly not sure how to finish.

If you've gotten far enough in algebra to be working on systems of equations, then you should have studied variables, word problems, and solving single equations. So you should have at least some how to work with variables to set up your equations. :wink:

As for solving ("how to finish"), one method might be to follow the instructions: review your book and class notes (and online resources) regarding setting up the matrix form of the system of equations, finding the inverse of the coefficient matrix, multiplying by this, and reading off the values of the variables. Then re-set, using the new system you created for part (c).

Eliz.

 

[Deleted member 4993]

Cajun Joe makes a gumbo that uses sausage, rice, and vegetables. The sausage costs $3 a pound, the rice costs $1.50 a pound, and the vegetables cost $0.75 a pound. Joe makes batches of gumbo that use a total of 20 pounds of ingredients and costs $1.50 per pound. Joe uses the same weight of rice as he does vegetables.

a. Write a system of equations to using x as the number of pounds of sausage used, y as the number of pounds of rice used, and z as the number of pounds of vegetables used. Then write a matrix equation to solve the system.

b. Use an inverse matrix to solve the system

c. Joe also makes a "meaty" version of his gumbo that uses the same amount of sausage as rice in each 20 pound batch and costs $1.65 a pound. Write a system of equations for the "meaty" version of Joe's gumbo. The use an inverse matrix to solve the system. Explain why the "meaty" version costs more per pound.

That sure seems like a big question to me and I'm not sure where to start and most certainly not sure how to finish.....

If you are far enough in algebra to tacke "inverse matrices" - then yo should definitely know how to start these problems. You are just refusing to think.

To start any word problem :

Start naming things (variables) - that you need to know:

Amount (lbs) of sausage (in a batch of gumbo) = S

Amount (lbs) of rice (in a batch of gumbo) = R

Amount (lbs) of vegetables (in a batch of gumbo) = V

So then your first equation is:

Joe makes batches of gumbo that use a total of 20 pounds of ingredients

S + R + V = 20 ....................................................................(1)

There are three unknowns - so you need three equations to solve them.

Write the other two equations and proceed.