Algebra II word problem help!?

Question

math problem: You want to order a deli platter for a sports banquet. You need 12 lbs of meat and cheese. You want twice as much meat as cheese on the platter and the same amount of ham and turkey. The price per pound is $4.95 for ham, $6.99 for turkey, $7.99 for roast beef, and $4.36 for cheese. How many pounds of each should you order if you plan to spend $64.24?

- We have been working with matrices and linear systems. So I know I should set it ups a linear system or a matrix but I have no clue what to do. I have been working on this for so long. Any help would be greatly appreciated.

Answer 1

okay, you have 4 unknowns:

let x = amount of cheese
y = amount of turkey
z = amount of ham
w = amount of roast beef

here's some equations:

y = z
y + z + w = 2x
495z + 699y + 799w + 436x = 6424
w + z + y + x = 12

If you want to set this up in a matrix, rewrite as follows for w,x,y,z:

0w + 0x +1y -1z = 0
1w - 2x + 1y +1z = 0
799w + 436x + 699y + 495z = 6424
1w +1x + 1y + 1z = 12

I hope that's enough to get you going! You have four equations with four unknows, so it shouldn't be impossible to solve.

Have fun with it!

Answer 2

I am assuming the $64.24 is the price before sales tax or we cannot answer the problem without knowing the sales tax rate.

Let's call T = weight of turkey; C = weight of cheese, H = weight of Ham, R = weight of roast beef with all weights in lbs.

we know these relationships exist

T = H - turkey and ham have same weight; I fold this in to all of the subsequent relationships

C = 2(T + H + R) = 2(2T + R) [ratio cheese to meet]
12 = C + T + H + R = C + 2T + R [12 lbs is tot weight]
64.24 = 4.36C + 6.99T + 4.95H + 7.99R
= 4.36C + T (6.99 + 4.95) + 7.99R [tot spent]

Now let's work with these two
C = 4T + 2R
12 = C + 2T + R and sub for C its equivalent 4T + 2R
12 = 6T + 3R or, solving for R
R = 4 - 2T
and C = 4T + 2(4-2T)
= 4T + 8 - 4T
= 8 - this is unusual but that is what the calculation shows; this is the weight of Cheese

Going to the last equation
64.24 = 4.36C + T (6.99 + 4.95) + 7.99R and sub
64.24 = 4.36(8) + T (6.99 + 4.95) + 7.99 (4-2T) or
64.24 - 4.36(8) - 4(7.99) = (6.99 + 4.95)T - 7.99(2)T
-2.6 = -4.04T or
T = 0.6436 lb

Since T = H, H is also 0.6436 lb

now go back and plug in to determine R;

Go over carefully what I did; it is just a series of equations; not that hard; I may have a math error here as I did not take time to double check; just work it one step at a time and all falls in place.

Answer 3

Let H=ham, T=turkey, R=roast beef , and C=cheese
1} H+T+R+C=12
2} H+T+R=2C
3} H=T
4} 4.95H+6.99T+7.99R+4.36C=64.24
Sub 3} into the rest
1} 2T+R+C=12
2} 2T+R=2C
4} 11.94T+7.99R+4.36C=64.24
rewrite 1} as 2T+R=12-C and plug into
2} 12-C=2C means 3C=12 C=4
sub that into 4} 11.94T+7.99R+4.36(4)=64.24
gives a new 4th equation of 11.94T+7.99R=46.8
sub C=4 into 1} for a new 2st equation 2T+R=4 or R=4-2T
sun that into 4} 11.94T+7.99(4-2T)=46.8
11.94T+31.96-15.98T=46.8
4.04T=17.12
T=
yikes! I have an error somewhere, if I find it, I will modify my answer.
Not sure where I made my error but the answer is ham=3, turkey=3, roast beef=2, cheese=4

Answer 4

Fun time with Gaussian Elimination, never had fun with ham and turkey, usually something stupid with money or balls.

Answer 5

I'm in Algebra I so I can't really help you. Good Luck though!

Answer 6

im in algebra one and i having a hard enough time with that copy your friends