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Class Scheduling Enormous State University's Math Department offers two courses: Finite Math and Applied Calculus. Each section of Finite Math has 30 students, and each section of Applied Calculus has 20 students. The department will offer a total of 50 sections in a semester, and 1,200 students would like to take a math course. How many sections of each course should the department offer in order to fill all sections and accommodate all of the students?

Class Scheduling Enormous State University's Math Department offers two courses: Finite Math and Applied Calculus. Each section of Finite Math has 30 students, and each section of Applied Calculus has 20 students. The department will offer a total of 50 sections in a semester, and 1,200 students would like to take a math course. How many sections of each course should the department offer in order to fill all sections and accommodate all of the students?

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.CT: Chapter Test
Problem 6CT: Wholesale distribution Ace Electronics, Hi-Fi Stereo, and CD World buy a total of 175 DVD players...
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Tutorial Exercise Class Scheduling Enormous State University's Math Department offers two courses: Finite Math and Applied Calculus. Each section of Finite Math has 30 students, and each section of Applied Calculus has 20 students. The department will offer a total of 50 sections in a semester, and 1,200 students would like to take a math course. How many sections of each course should the department offer in order to fill all sections and accommodate all of the students? Step 1 Read the problem carefully--perhaps several times-to make sure all words and ideas are understood. Identify what we are asked to find, and choose variables to represent those quantities. The unknowns here are x, the number of sections of Finite Math to be offered and y, the number of sections of Applied Calculus to be offered. Notice that there are two constraints; the total number of sections to be offered is fixed, and so is the total number of students. The two constraints can be used to find two equations relating x and y to each other. To begin, consider the fixed total number of sections to be offered. Because there will be 50 sections, (the number of sections of Finite Math) + (the number of sections of Applied Calculus) = 50. Therefore, x + y =
Transcribed Image Text:Tutorial Exercise Class Scheduling Enormous State University's Math Department offers two courses: Finite Math and Applied Calculus. Each section of Finite Math has 30 students, and each section of Applied Calculus has 20 students. The department will offer a total of 50 sections in a semester, and 1,200 students would like to take a math course. How many sections of each course should the department offer in order to fill all sections and accommodate all of the students? Step 1 Read the problem carefully--perhaps several times-to make sure all words and ideas are understood. Identify what we are asked to find, and choose variables to represent those quantities. The unknowns here are x, the number of sections of Finite Math to be offered and y, the number of sections of Applied Calculus to be offered. Notice that there are two constraints; the total number of sections to be offered is fixed, and so is the total number of students. The two constraints can be used to find two equations relating x and y to each other. To begin, consider the fixed total number of sections to be offered. Because there will be 50 sections, (the number of sections of Finite Math) + (the number of sections of Applied Calculus) = 50. Therefore, x + y =
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