Can you guys help me out wit this word problem?

Question

You want to order a deli platter for a sports banquet. You need 12 pounds of meat and cheese. You want twice as much meat as cheese on the platter and an equal 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 $69.24?

I have thought this over for about an hour and I just now realized that the word 'meat', in the first part refers to the beef, the turkey, AND the ham =(. I can't believe I've only gotten this far, everyone else in my class understood it, but I'm stumped. I need to make this data into equations so I can solve it using matrices. Don't tell me the answer, just sort of point me in the right direction if you can. Thanks ahead of time.

Answer 1

Start with the easy part, how much meat and cheese.

Let c = cheese
Let m = meat

m = 2c
m + c = 12
2c + c = 12
3c = 12
c = 4
m = 8

So you need 4 lbs of cheese and 8 lbs of meat.

The 4 lbs of cheese will cost 4 x $4.36 = $17.44

That leaves $51.80 for the meat.

Let h = ham
Let t = turkey
Let r = roast beef

h + t + r = 8
but h = t so substitute:
2t + r = 8

Next equation:
4.95h + 6.99t + 7.99r = $51.80

Again h = t, so substitute:
(4.95 + 6.99)t + 7.99r = $51.80
11.94t + 7.99r = 51.80

Now you have two equations and two unknowns... you can solve it with matrices or just regular algebra.

2t + r = 8
2t = (8-r)
t = (8-r)/2
11.94*(8-r)/2 + 7.99r = 51.80
5.97*(8-r) + 7.99r = 51.80
47.76 - 5.97r + 7.99r = 51.80
2.02r = 51.80 - 47.76
2.02r = 4.04
r = 2

So you need:
2 lbs of roast beef = $15.98
3 lbs of turkey = $20.97
3 lbs of ham = $14.85
4 lbs of cheese = $17.44

Total = $69.24