Answer:
a) System of equations will be: [tex]x+y=500\: and\:5x+2y=1789[/tex]
b) Number of adult tickets sold = 263
Number of students tickets sold = 237
Step-by-step explanation:
Let:
Number of adult tickets sold = x
Number of students tickets sold = y
a)
As Marc sold total 500 tickets, the expression will be: [tex]x+y=500[/tex]
Student tickets cost $2 and adult tickets cost $5. Marc's sales totalled $1,789.
The expression will be: [tex]5x+2y=1789[/tex]
So, system of equations will be: [tex]x+y=500\: and\:5x+2y=1789[/tex]
b)
Solve the system to find value of x and y
Let:
[tex]x+y=500--eq(1)\\5x+2y=1789--eq(2)[/tex]
Multiply equation 1 by 2 and subtract
[tex]2x+2y=1000\\5x+2y=1789\\-\:\:\:-\:\:\:\:\:\:\:\:\:-\\------\\-3x=-789\\x=\frac{-789}{-3}\\x=263[/tex]
We get value of x = 263
Now finding value of y by putting value of x in eq(1)
[tex]x+y=500\\263+y=500\\y=500-263\\y=237[/tex]
We get value of y = 237
Number of adult tickets sold = x = 263
Number of students tickets sold = y = 237
