Answer: The price of a ticket for the gold section exceeds the price for a ticket for the silver section by 8 dollars.
Step-by-step explanation: Given that the following system of equations relates the ticket price , in dollars, for seats in the silver (x) and gold (y) sections at a rock concert :
[tex]x+2y=82~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x+y=96~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
We are to find by how much the price of a ticket for the gold section exceed the price for a ticket for the silver section.
First, we will solve the given system of equations as follows :
From equation (i), we have
[tex]x+2y=82\\\\\Rightarrow x=82-2y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of x from equation (iii) in equation (ii), we get
[tex]3x+y=96\\\\\Rightarrow 3(82-2y)+y=96\\\\\Rightarrow 246-6y+y=96\\\\\Rightarrow 246-5y=96\\\\\Rightarrow 5y=246-96\\\\\Rightarrow 5y=150\\\\\Rightarrow y=\dfrac{150}{5}\\\\\Rightarrow y=30.[/tex]
From equation (ii), we get
[tex]x=82-2\times30=82-60=22.[/tex]
So, the price of a ticket for a ticket for the silver section = 22 dollars
and
the price of a ticket for a ticket for the gold section = 30 dollars.
Therefore, we get
[tex]y-x=30-22=8.[/tex]
Thus, the price of a ticket for the gold section exceeds the price for a ticket for the silver section by 8 dollars.
