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 45 sections total, there are 4,700 students who would like to take a course, and there are 58 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?

 

 

answer the following:

 

Ancient History ? sections

Medieval History ? sections

Modern History ? sections

?Ancient History =  10 sectionsMedieval History =  22 sectionsModern History =  13 sections?

Step-by-step explanation

?let x,y,z be the no. of section of Ancient, Medieval, and Modern History respetively.Condition 1: The department is allowed to offer 45 sections totalx + y + z = 45 Condition 2: there are 4,700 students who would like to take a course.Sections of Ancient History have 100 students each, sections of Medieval History hold 50 students each, and sections ofModern History have 200 students each. 100x + 50y + 200z = 4700 Condition 3: there are 58 professors to teach them. Modern History sections are taught by a team of two professors, while Ancient and Medieval History need only one professor per section. x + y + 2z = 58 ? ?Systems of Equations: x + y + z = 45 equation 1100x + 50y + 200z = 4700 equation 2x + y + 2z = 58 equation 3perform subtraction: equation 3 - equation 1(x+y+2z)−(x+y+z)=58−45z = 13substitute z = 13 in equation 1 and equation 2 x+y+13=45⇒x+y = 32equation 4100x+50y+200(13)=4700⇒ 100x+50y = 2100equation 5perform subtraction: equation 5 - (50×equation 4)(100x+50y)−50(x+y)=2100−50(32)50x=500x = 10substitute x = 10 in equation 410+y=32⇒y = 22 ?

?Ancient History =  10 sectionsMedieval History =  22 sectionsModern History =  13 sections?

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