You own a hamburger franchise and are planning to shut down operations for the d

Question

You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 13 buns, 18 defrosted beef patties, and 12 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=

Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40 students and earns the college $60,000, while each section of Computer Methods has 10 students and earns the college $29,000. Assuming the college wishes to offer a total of seven sections, accommodate 220 students, and bring in $298,000 in revenues, how many sections of each course should it offer?
Finite Math section(s)=

Applied Calculus section(s)=

Computer Methods section(s)=

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 43 sections total, there are 4,700 students who would like to take a course, and there are 56 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

Suppose in one year, total revenues from digital sales of pop/rock, tropical (salsa/merengue/cumbia/bachata), and urban (reggaeton) Latin music in a certain country amounted to $21 million. Pop/rock music brought in twice as much as the other two categories combined and $9 million more than tropical music. How much revenue was earned from digital sales in each of the three categories?
pop/rock music$ million

tropical music$ million

urban Latin music$ million

plain burge deuble chesoeburgers egular cheeseburgr ections) apied Cokulus eections) The Evaaue State Usvesty History Deperement offers three ourses-Ardest Hedeval end Matern Madeval atory odom atory aach af the three catagoria? cpradk manic tropical usic urban Latn muc × nilion

Explanation / Answer

multiple questions posted.please post each question seperately

1)

let number of plain burgers=x,double cheeseburgers=y,regular cheeseburgers=z

equations are 1x+ 2y +1z = 18 ,1x+1y+1z=13,2y+1z = 12

1x+ 2y +1z -1x - 1y- 1z= 18-13

=> y =5

2y+1z = 12,y=5

=>(2*5)+z = 12

=>10+z=12

=>z =2

1x+1y+1z=13 , y =5, z=2

=>x +5+2 =13

=> x= 13-7

=>x= 6

so ,you should make

plain burgers= 6

double cheeseburgers= 5

regular cheeseburgers= 2

================================================

2)

let number of sections of Finite Math=x , Applied Calculus= y , Computer Methods =z

equations are x+y+z=7, 40x+40y+10z =220 , 40000x+ 60000y +29000z= 298000

=> x+y=7-z, x+y+(1/4)z =(11/2) , 40x+ 60y +29z= 298

=>7-z+(1/4)z =(11/2)

=>z-(1/4)z =7-(11/2)

=>(3/4)z =(3/2)

=>z=2

x+y=7-z ,z=2

=>x+y=7-2

=>x+y=5

=> y =5-x

40x+ 60y +29z= 298, y=5-x, z=2

=>40x+ 60(5-x) +29*2= 298

=>40x +300 -60x +58= 298

=>20x = 60

=>x=3

y =5-x ,x=3

=> y =5-3

=>y =3

Finite Math section(s)= 3

Applied Calculus section(s)=2

Computer Methods section(s)=2

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