How many students are on the trip?

Question

There are 4 times as many students as teachers on a trip.  There are a total of 80 people.  How many are students?  Solve using system of equations by substitution or elimination.

Answer 1

Let:

   s = number of students

   t = number of teachers

 

Translate:

   "4 times as many students as teachers"      means     s = 4t    [eq1]

   " total of 80 people"      means     s + t = 80     [eq2]

   "How many are students?"      means     report s

 

Substitution:

     Use one equation to solve for one variable, then substitute into the other equation to solve for the other variable.

   t = 80 - s        [from eq2]

   s = 4(80-s)     [put that into eq1]

   s = 320 - 4s      [distribute]

   5s = 320        [add 4s to both sides]

     s = 64      {There were 64 students]

 

Elimination:

       Add/subtract equations with the same coefficient one variable to eliminate it.

   4s   +  4t   =   320     [4*eq2]

     s   -  4t   =       0      [from eq1]

  --------------------    [eliminate 4 using addition]

   5s             =   320

     s            =  64

 

Check:

    s = 4t

    64 = 4(16)     so t=16

 

    s + t = 80

    64 + 16 = 80

  Yes:

 

Answer 2

This situation fits the pattern for systems of equations because there are two unknowns, but also enough information to set up two equations.

You can try something like this:   use s= number of students   and  t = number of teachers.

There are a total of 80 people, so   80= s+t

You also know  that, proportionally, if there are 2 teachers, there are 8 students.  If there are 3 teachers, there are 12 students (neither of these are the answer, obviously, because they don't add up to 80).  This means s=4t.

 

Write in the comments if you're looking for either substitution or elimination assistance. :)