Admission to a baseball game game is $3.00 for general admission and $3.50 for reserved seats. The receipts were $2907.50 for 906 admissions. How many of each ticket were sold? (round to the nearest integer if necessary)

Question

Admission to a baseball game game is $3.00 for general admission and $3.50 for reserved seats.  The receipts were $2907.50 for 906 admissions.  How many of each ticket were sold? (round to the nearest integer if necessary)

anonymous · Answer

We need to create s system of equations to solve. For the first equation, lets look at the number of tickets sold. Let x represent the general seats, and y represent the reserved seats.  Then we know that:

x + y = 906

because there was 906 addmissions.
Now, looking at the price instead, we have:

3.00x + 3.50y = 2907.50

because 2907.50 was spent in total on those tickets.

anonymous · Answer

So now, we need to solve this system, and there are a couple of ways to do that. Im going to do it by substitution, but you can do it in whatever method you please.  So looking at the first equation, im going to solve for x:
$$x+y = 906 \Rightarrow x = 906-y$$
Now im going to substitute that value of x into the second equation, and solve for y:
$$3.00x+3.50y=2907.50 \Rightarrow 3.00(906-y)+3.50y = 2907.50$$
$$\Rightarrow 2718.00-3.00y+3.50y = 2907.50 \Rightarrow .50y = 189.50 \Rightarrow y = 379$$

anonymous · Answer

Now, y represented the number of reserved seats, so we still need to figure out the number of general admission seats. That would be:

906 - 379 = 527

and now you are done :)