Question

HELP PLEASEEEE !!!!

Answer 1

Gold Section is 8 dollars more.

Answer 2

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 :

$x+2y=82~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x+y=96~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

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

$x+2y=82\\\\\Rightarrow x=82-2y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of x from equation (iii) in equation (ii), we get

$3x+y=96\\\\\Rightarrow 3(82-2y)+y=96\\\\\Rightarrow 246-6y+y=96\\\\\Rightarrow 246-5y=96\\\\\Rightarrow 5y=246-96\\\\\Rightarrow 5y=150\\\\\Rightarrow y=\dfrac{150}{5}\\\\\Rightarrow y=30.$

From equation (ii), we get

$x=82-2\times30=82-60=22.$

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

$y-x=30-22=8.$

Thus, the price of a ticket for the gold section exceeds the price for a ticket for the silver section by 8 dollars.