A community college offers courses in Applied Algebra, Business Calculus, and Statistics. Each section of Applied Algebra has 50 students and earns the college $20,000 in revenue. Each section of Business Calculus has 20 students and earns the college $50,000 in revenue. Each section of Statistics has 30 students and earns the college $60.000 in revenue. Assuming the college wishes to offer a total of 7 sections, accommodate 230 students, and bring in $320,000 in revenue, how many sections of each course should they offer? ? sections of Applied Algebra ? sections of Business Calculus ? sections of Statistics

Question

A community college offers courses in Applied Algebra, Business Calculus, and Statistics. Each section of Applied Algebra has 50 students and earns the college $20,000 in revenue. Each section of Business Calculus has 20 students and earns the college $50,000 in revenue. Each section of Statistics has 30 students and earns the college $60.000 in revenue. Assuming the college wishes to offer a total of 7 sections, accommodate 230 students, and bring in $320,000 in revenue, how many sections of each course should they offer?  ? sections of Applied Algebra   ? sections of Business Calculus   ? sections of Statistics

rodclassique4r · Accepted Answer

Step 1  let x ,y and z be the number of sections of Applied Algebra, Business Calculus and Statistics.  Total number of sections is 7, so x+y+z=7 ... (1)  Total number of students is 230, so  50x+20y+30z=230  5x+2y+3z=23 ...(2)  Total revenue is 320,000, so  20,000x+50,000y+60,000z=320,000  2x+5y+6z=32 ...(3)  Step 2  Subtract equation (2) from 5 times equation (1)  3y+2z=12 ...(4)  Subtract twice the equation (1) from equation (3)  3y+4z=18 ...(5)  Subtract equation (4) from equation (5)  2z=6  z=3  From equation (4)  3y+2z=12  3y+2(3)=12  3y+6=12  3y=6  y=2  From equation (1)  x+y+z=7  x+2+3=7  x=2  Step 3  Ans: The number of sections of Applied Algebra, Business Calculus and Statistics are 2,2 and 3 respectively.

yotaniwc · Accepted Answer

Step 1  Assume number of sections in applied algebra, Business calculus and Statistics be a, b and s respectively.  Step 2  Total number of sections =7  a+b+s=7 ...(1)  Total number of students =230  50a+20b+30s=230  5a+2b+3s=23 ...(2)  Total revenue =320,000  20,000a+50,000b+60,000s=320,000  2a+5b+6s=32 ...(3)  Step 3  Substitute a=7−b−s into equation (2).  5(7−b−s)+2b+2s=23  35−5b−5s+2b+3s=23  −3b−2s=−12  3b+2s=12 ...(4)  Substitute a=7−b−s into equation (3).  2(7−b−s)+5b+6s=32  14−2b−2s+5b+6s=32  3b+4s=18 ...(5)  Step 4  Subtract equation (4) from equation (5).  (3b+4s)−(3b+2s)=18−12  2s=6  s=3  Substitute s=3 into the equation (4).  3b+2(3)=12  3b+6=12  3b=6  b=2  Substitute s=3 and b=2 into the equation (1).  a+2+3=7  a=2  Step 5  Answer:  2 sections of applied algebra  2 sections of business calculus  3 sections of statistics

nick1337 · Accepted Answer

Step 1 Given information Applied Algebra has 40 student and revenue is $70,000 Business Calculus has 30 student and revenue is $40,000 Statistics has 20 student and revenue is $50,000 And total number of section is 11 and total revenue is $550,000 We have to find the sections of each courses. Let the number of section of Applied Algebra, Business Calculus and Statistics is x,y and z respectively. According to given condition Since, total number of sections is 11 Hence, x+y+z=11 ...(1) And total number of student is 300 NSK Hence, 40x+30y+20z=300 And total revenue is $550,000 Hence, 70,000x+40,000y+50,000z=550,000 ...(3) Step 2 NSK Subtract equation from equation (2), we get 20x+10y=80 ...(4) Now, subtract equation 50,000×(1) from equation (3), we get 20,000x−10,000y=0 ...(5)  Solve equation (5) ⇒20,000x−10,000y=0 ⇒20,000x=10,000y ⇒x=10,00020,000y ⇒x=y2 Step 3 Now, substitute x=y2 in equation (4) 20×y2+10y=80 10y+10y=80 20y=80 y=8020 y=4 Hence, y=4 Substitute y=4 in x=y2 x=42 =2 Hence, x= Now, substitute x=2 and y=4 in equation (1) ⇒2+4+z=11 ⇒6+z=11 ⇒z=11−6 ⇒z=5 Hence, z=5 Step 4 Therefore, 2 section of Applied Algebra 4 section of Business Calculus 5 section of Statistic

A community college offers courses in Applied Algebra, Busin

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