Enormous State University's Math Department offers two courses: Finite Math and Applied Calculus. Each section of Finite Math has 60 students, and each section of Applied Calculus has 50 students. The department will offer a total of 110 sections in a semester, and 6,000 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

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29-01-2021
Mathematics

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Enormous State University's Math Department offers two courses: Finite Math and Applied Calculus. Each section of Finite Math has 60 students, and each section of Applied Calculus has 50 students. The department will offer a total of 110 sections in a semester, and 6,000 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

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nuhulawal20 nuhulawal20 · Answer 1 · 2021-02-01T03:40:07+01:00

Answer:

the department should offer 50 sections of finite math and 60 section of applied calculus in order to fill all sections and accommodate all of the students

Step-by-step explanation:

Given the data in the question'

let x represent number of sections of finite math while y represent number of section of applied calculus.

as 6000 student will like to take math course;

in each section, finite math has 60 students while applied calculus has 50 students

so;

60x + 50y = 6000 --------------lets this be equ 1

we also know that; there are 110 sections in a semester

so;

x + y = 110 ------------------ let this be equ 2

multiply equation 2 by ( - 60 )

-60x + -60y = -6600 --------------- let this be equ 3

now lets add equation 1 and 3

0 - 10y = -600

-10y = -600

divide both sides by (-10)

-10y/-10 = -600/-10

y = 60

now lets substitute value of y in equation 2

x + 60 = 110

x = 110 - 60

x = 50

Therefore, the department should offer 50 sections of finite math and 60 section of applied calculus in order to fill all sections and accommodate all of the students