Solve using a system of three linear equations.
-A deli sells three sizes of roast beef sandwiches: the small roast beef sandwich contains 4 ounces of meat and sells for $3.00; the regular roast beef sandwich contains 7 ounces of meat and sells for $3.50; and the large
Roast beef sandwich contains 9 ounces of meat and sells for $4.00. A customer requests a selection of each size
For a reception. She and the manager agree on a combination of 54 sandwiches made from 20 pounds 2 ounces
Of roast beef for a total cost of $181. How many of each size sandwich will be in this combination? (Note: 1
Pound = 16 ounces)
A)20 small sandwiches, 18 medium sandwiches, 16 large sandwiches.
B)22 small sandwiches, 28 medium sandwiches, 4 large sandwiches.
C)24 small sandwiches, 22 medium sandwiches, 8 large sandwiches.
D)26 small sandwiches, 16 medium sandwiches, 12 large sandwiches.

Question

Quizplus · Accepted Answer

First, convert 20 pounds 2 ounces to ounces: 20 pounds * 16 ounces/pound + 2 ounces = 322 ounces. Let x, y, and z represent the number of small, medium, and large sandwiches, respectively. We have three equations:1) x + y + z = 54 (total sandwiches)2) 4x + 7y + 9z = 322 (total ounces of meat)3) 3x + 3.5y + 4z = 181 (total cost)Solving this system of equations yields x = 24, y = 22, and z = 8, which corresponds to 24 small sandwiches, 22 medium sandwiches, and 8 large sandwiches.

Solve Using a System of Three Linear Equations