I have been trying for awhile, but I can't figure this out. I don't need the answer, I just need to know how to write the system.

Question

You want to order a deli platter for a sports banquet. You need 12 pounds of meat (ham, turkey, and roast beef) and cheese total. You want twice as much meat as cheese on the platter. You want the same amount of ham as 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? Write a system of 4 equations using 4 variables.

Answer 1

Let H be the amount of ham, T be the amount of turkey, B be the amount of roast beef, and C be the amount of cheese. All amounts are assumed to be in pounds as asked by the problem.

 

Here are the equations for the constraints in order they are given.

 

Constraint 1: H + T + B + C = 12

 

Constraint 2: H + T + B = 2C

 

Constraint 3: H = T

 

Constraint 4: 4.95H + 6.99T + 7.99B + 4.36C = 69.24

 

Now solve this system for the answer.

Answer 2

Since the prices of the four ingredients are already given, your independent variables are only how much quantities of ham, turkey, roast beef and cheese you need for the deli platter. There are certain conditions given to complete the deli platter and you have to write the system of equations using those.

 

First, assume following pounds of each ingredient you need:

 

Ham = h

Turkey = t

Roast beef = b

Cheese = c

 

Since you can't spend more than $69.24, your first equation is:

 

4.95h + 6.99t + 7.99b + 4.36c = 69.24.....................(1)

 

Since we need 12 pounds of meat and cheese, our next equation is:

 

h+t+b+c = 12............................................................(2)

 

We need twice as much meat as cheese, which gives us our next equation:

 

h+t+b = 2c................................................................(3)

 

We also want same amount of ham as turkey, which gives our fourth and final equation:

 

h = t..........................................................................(4)

 

I hope this helps you. Thanks.