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The junior and senior students at Mathville High School are going to present an exciting musical entitled, "Math, What is it Good For?". A large group of students came out to an information meeting. After a brief introduction to the musical, 15 senior students decided that it was not for them and they left. At that point, twice as many junior students as senior students remained. Later in the meeting, after the 15 senior students had left, of the junior students and of the remaining senior students also left. This left 8 more senior students than junior students. All of the remaining students stuck it out and went on to produce an amazing product. How many students remained to perform in the school musical, "Math, What is it Good For?"

Respuesta :

Edufirst

Some parts are missing in the queston. Find attached the picture with the complete question

Answer:

                   [tex]\large\boxed{\large\boxed{161}}[/tex]

Explanation:

Let's put the information in a table step-by step.

                                                (number of remaining students)

                                                        Juniors          Seniors

Condition

  • Initially                                           J                     S
  • 15 seniors left                                                   S - 15
  • Twice juniors as seniors         2(S - 15)
  • 3/4 of the juniors left              1/4×2(S - 15)
  • 1/3 of seniors left                                             2/3×(S - 15)

At the end, there were 8 more seniors than juniors:

  • 2/3×(S - 15) -  1/4×2(S - 15) = 8

Now you have obtained one equation, which you can solve to find S, the number of senior students, and then the number of junior students.

Solve the equation:

[tex]2/3\times (S - 15) - 1/4\times 2(S - 15) = 8[/tex]

  • Mutilply all by 12:

[tex]8(S - 15)-6(S - 15)=96[/tex]

  • Distribution property:

[tex]8S-120-6S-90=96[/tex]

  • Addtion property of equalities:

[tex]8S-6S=96+120+90[/tex]

  • Add like terms:

[tex]2S=306[/tex]

  • Division property of equalities:

[tex]S=306/2=153[/tex]

That is the number of senior students that came out to the information meeting, but the number of students remaining to perform in the school musical is (from the table above):

[tex]2/3\times (S-15)+1/4\times 2(S-15)[/tex]

Just substitute S with 153 fo find the number of students that remained to perfom in the musical:

          [tex]2/3\times (153-15)+1/4\times 2(153-15)\\ \\ 2/3(138)+1/2(138)[/tex]

          [tex]161[/tex]

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