a concession stand at a city park sells hamburgers, hot dogs, and drinks. Three patrons buy the food and drink combinations denoted in the following table. Patron 1 spends $11, patron 2 pays $5 for the food, and the price of the food for patron 3 is $22. Let x, y and z represent the cost for a hamburger, a hot dog, and a drink, respectively. Set up a system of equations to solve for x, y and z. Then, set up the augmented matrix for the system and solve the system. Explain the solution in the context of the problem. Write the answer in a complete sentence. Patron Hamburgers Hot Dogs Drinks 1 1 1 5 2 0 1 2 3 3 1 11 a. Identify the variables of the problem using x, y and z.
a concession stand at a city park sells hamburgers, hot dogs, and drinks. Three patrons buy the food and drink combinations denoted in the following table. Patron 1 spends $11, patron 2 pays $5 for the food, and the price of the food for patron 3 is $22. Let x, y and z represent the cost for a hamburger, a hot dog, and a drink, respectively. Set up a system of equations to solve for x, y and z. Then, set up the augmented matrix for the system and solve the system. Explain the solution in the context of the problem. Write the answer in a complete sentence.
Patron Hamburgers Hot Dogs Drinks
1 1 1 5
2 0 1 2
3 3 1 11
a. Identify the variables of the problem using x, y and z.
b. Determine the system of equations to be solved.
c. Solve the system of equations using Gauss-Jordan Elimination.
d. Explain the solution in the context of the problem. Write the answer in a complete sentence.
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