Solve Problems Using Systems in Three Variables
-A deli sells three sizes of roast beef sandwiches: the small roast beef sandwich contains 6 ounces of meat and sells for $3.50; the regular roast beef sandwich contains 9 ounces of meat and sells for $4.00; and the large roast beef sandwich contains 13 ounces of meat and sells for $4.50. A customer requests a selection of each size for a reception. She and the manager agree on a combination of 42 sandwiches made from 23 pounds 10 ounces of roast beef for a total cost of $164. How many of each size sandwich will be in this combination? (Note: 1 pound = 16 ounces)
A) 16 small sandwiches, 18 medium sandwiches, 8 large sandwiches.
B) 18 small sandwiches, 12 medium sandwiches, 12 large sandwiches.
C) 12 small sandwiches, 14 medium sandwiches, 16 large sandwiches.
D) 14 small sandwiches, 24 medium sandwiches, 4 large sandwiches.

Question

Quizplus · Accepted Answer

To solve this, we set up a system of equations based on the information given: Let x be the number of small sandwiches, y the number of medium sandwiches, and z the number of large sandwiches. We have three equations: 1) x + y + z = 42 (total sandwiches), 2) 6x + 9y + 13z = 23*16 + 10 (total meat in ounces), and 3) 3.5x + 4y + 4.5z = 164 (total cost). Solving this system gives us x = 16, y = 18, and z = 8.