1- You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 12 buns, 18 defrosted beef patties, and 14 opened cheese slices. Rather than throw them out, you decide to use them to make burgers that you will sell at a discount. Plain burgers each require 1 beef patty and 1 bun, double cheeseburgers each require 2 beef patties, 1 bun, and 2 slices of cheese, while regular cheeseburgers each require 1 beef patty, 1 bun, and 1 slice of cheese. How many of each should you make?

plain burgers

double cheeseburgers

regular cheeseburgers

2-
The Enormous State University History Department offers three courses—Ancient, Medieval, and Modern History—and the chairperson is trying to decide how many sections of each to offer this semester. The department is allowed to offer 48 sections total, there are 5,400 students who would like to take a course, and there are 65 professors to teach them. Sections of Ancient History have 100 students each, sections of Medieval History hold 50 students each, and sections of Modern History have 200 students each. Modern History sections are taught by a team of two professors, while Ancient and Medieval History need only one professor per section. How many sections of each course should the chair schedule in order to offer all the sections that they are allowed, accommodate all of the students, and give one teaching assignment to each professor? HINT [See Example 2.] (Assume each section has the maximum number of students allowed.)

Ancient History sections

Medieval History sections

Modern History sections

3- Halmar the Great has boasted to his hordes of followers that many a notorious villain has fallen to his awesome sword: His total of 500 victims consists of evil sorcerers, trolls, and orcs. These he has slain with a total of 600 mighty thrusts of his sword; evil sorcerers and trolls each requiring two thrusts (to the chest) and orcs each requiring one thrust (to the neck). When asked about the number of trolls he has slain, he replies, "I, the mighty Halmar, despise trolls four times as much as I despise evil sorcerers. Accordingly, four times as many trolls as evil sorcerers have fallen to my sword!" How many of each type of villain has he slain?
sorcererstrollsorcs

4-
The following table shows the amount spent by four U.S. airlines to fly one available seat 1 mile in the second quarter of 2014.† Set up a system and then solve using technology. HINT [See the technology note accompanying Example 1.]

Airline United
Continental American JetBlue Southwest

Cost (¢) 14.9 14.6 11.9 12.4

Suppose that, on a 3,000-mile New York to Los Angeles flight, United Continental, American, and Southwest flew a total of 250 empty seats, costing them a total of $106,095. If United Continental had three times as many empty seats as American, how many empty seats did each of these three airlines carry on its flight?

United Continental empty seats

American empty seats

Southwest empty seats

Question

1- You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 12 buns, 18 defrosted beef patties, and 14 opened cheese slices. Rather than throw them out, you decide to use them to make burgers that you will sell at a discount. Plain burgers each require 1 beef patty and 1 bun, double cheeseburgers each require 2 beef patties, 1 bun, and 2 slices of cheese, while regular cheeseburgers each require 1 beef patty, 1 bun, and 1 slice of cheese. How many of each should you make?

plain burgers

double cheeseburgers

regular cheeseburgers

2-

The Enormous State University History Department offers three courses—Ancient, Medieval, and Modern History—and the chairperson is trying to decide how many sections of each to offer this semester. The department is allowed to offer 48 sections total, there are 5,400 students who would like to take a course, and there are 65 professors to teach them. Sections of Ancient History have 100 students each, sections of Medieval History hold 50 students each, and sections of Modern History have 200 students each. Modern History sections are taught by a team of two professors, while Ancient and Medieval History need only one professor per section. How many sections of each course should the chair schedule in order to offer all the sections that they are allowed, accommodate all of the students, and give one teaching assignment to each professor? HINT [See Example 2.] (Assume each section has the maximum number of students allowed.)

Ancient History sections

Medieval History sections

Modern History sections

3- Halmar the Great has boasted to his hordes of followers that many a notorious villain has fallen to his awesome sword: His total of 500 victims consists of evil sorcerers, trolls, and orcs. These he has slain with a total of 600 mighty thrusts of his sword; evil sorcerers and trolls each requiring two thrusts (to the chest) and orcs each requiring one thrust (to the neck). When asked about the number of trolls he has slain, he replies, "I, the mighty Halmar, despise trolls four times as much as I despise evil sorcerers. Accordingly, four times as many trolls as evil sorcerers have fallen to my sword!" How many of each type of villain has he slain?

sorcererstrollsorcs

4-

The following table shows the amount spent by four U.S. airlines to fly one available seat 1 mile in the second quarter of 2014.† Set up a system and then solve using technology. HINT [See the technology note accompanying Example 1.]

Airline	United Continental	American	JetBlue	Southwest
Cost (¢)	14.9	14.6	11.9	12.4

Suppose that, on a 3,000-mile New York to Los Angeles flight, United Continental, American, and Southwest flew a total of 250 empty seats, costing them a total of $106,095. If United Continental had three times as many empty seats as American, how many empty seats did each of these three airlines carry on its flight?

United Continental empty seats

American empty seats

Southwest empty seats

Accepted Answer

* ANSWER :- 
* According to guidelines I have answered one question ie first question only... please…