A total of 937 people attend the play. Admission was $2.00 for adults and $0.75 for students. The totral ticket sales amounted to $1,109. How many students and adults attended the school play? - Applying Linear Systems in the Real World

x = students

y = adults

Linear Systems of Equations :

x + y = 937

0.75x + 2y = 1,109

Step-by-step explanation:

Step 1 : eliminate one of the variables

x + y = 937

0.75x + 2y = 1,109

-2(x + y = 937) = -2x - 2y = -1874

-2x - 2y = -1874

0.75x + 2y = 1109

We can eliminate y since -2y + 2y = 0

Step 2: Find x number of students.

-2x = -1874

+0.75x = 1109

-1.25x = -765

= 612 students attended

     -1.25

937 - 612 = 325 adults

Check Answer :

612 x 0.75 = $459

325 x 2 = $650

$650 + $459 = $1,109

Therefore, there will be 612 students attending and 325 adults.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

answer: it is d

step-by-step explanation: