Question

More info in the comments. Linear System's?

Answer 1

There were 26,000 people at a ball game in Los Angeles. The day’s receipts were $204,000. How many people paid $14 for reserved seats and how many people paid $6 for general admission? Write a linear system to solve the problem, letting r represent the number of reserved seats sold and g the number of general admission tickets sold.

Answer 2

The price for a reserved seat is \($14\).
The total amount earned from reserved seat tickets is \($14r\), where \(r\) is the NUMBER OF PEOPLE who purchased reserved seat tickets.

The price for general admission is \($6\).
The total amount earned from general admission tickets is \($6g\), where \(g\) is a different number of people, who purchased general admission tickets.

So the total amount of money earned from tickets was \($204,000\).
This amount is equal to the total amount from reserved seat tickets and that from general admission tickets.

We can write it like this,\[\large 204,000=14r+6g\]

They gave us some more information.
Remember how we decided that \(r\) and \(g\) would represent the reserved and general admissions respectively?

Well they told us that the TOTAL NUMBER OF PEOPLE that attended the game were \(26,000\). This total is the SUM of the people who purchased either reserved and general admissions.

We can write it like this,
\[\large 26,000=r+g\]

Answer 3

So we have a system of 2 equations, and 2 unknowns.\[\large 204,000=14r+6g\]\[\large 26,000=r+g\]

Answer 4

From here, we can solve the system by one of two methods.
Either by \(\textbf{substitution}\) or by \(\textbf{elimination}\).

Are you familiar with either of these methods? :)

Answer 5

Oh wow. That's a wonderful explanations. Yeah I know how to do those methods! Thank you this helped a bunch!!!!

Answer 6

*Explanation

Answer 7

Ok cool! \:D/