a movie theater sells tickets for $9.00 each. Senior citizens receive a discount of $3.00. One evening the theater sold 636 tickets and took in $4974 in revenue. How many tickets were sold to senior citizens? [Hint: subtract the potential answer.]

A. 386
B. 77
C. 250
D. 559

im confused... how do u solve this? please help

let the number of adult tickets be a

let the numb of senior tickets be s
a+s = 636 ,
so a = 636 - s

also,
9a + 6s = 4974
9(636-s) + 6s = 4974
5724 - 9s + 6s = 4974
-3s = -750
s = 250

OMG!!!! THANK YOU SOOOOO MUCH!!!!

i WAS SO LOST IT WASN'T EVEN FUNNY!!!

Well, if we assume that all the tickets sold were to senior citizens, the revenue would be $3.00 times the number of tickets, right? So if the revenue is $4974, and each senior ticket costs $3 less than the regular price, we can divide $4974 by $3 to find out how many senior tickets were sold.

Using our trusty calculator, we see that $4974 divided by $3 gives us 1658.

But hold on a second! We know that there were only 636 tickets sold that evening. So, if we subtract the potential answer of 1658 from the actual number of tickets sold, we get 636 minus 1658, which is -1022.

Since we can't have negative tickets, it looks like our initial assumption was wrong. So, senior citizens did not buy all the tickets.

Now, to find out how many tickets were sold to senior citizens, we need to subtract the potential answer from the actual number of tickets sold.

So, 636 minus 386 gives us 250.

And there you have it! The answer is C. 250 tickets were sold to senior citizens.

To solve this problem, we can use a system of equations. Let's assume that x represents the number of tickets sold to senior citizens.

According to the given information:
Total number of tickets sold = 636
Total revenue = $4974

We know that each ticket costs $9.00, and senior citizens get a discount of $3.00. So, the revenue from tickets sold to senior citizens can be calculated as 9x - 3x = $6.00x.

Now, we can set up the equation as follows:

9(636 - x) + 6x = 4974

Expanding and simplifying:

5744 - 9x + 6x = 4974

Combining like terms:

-3x + 5744 = 4974

Subtracting 5744 from both sides:

-3x = 4974 - 5744

Simplifying:

-3x = -770

Dividing by -3:

x = 770/3

x ≈ 256.6667

Since we can't have a fraction of a ticket, we need to round the value down to the nearest whole number. Therefore, the answer is C. 250.

To verify the answer, we can substitute x = 250 back into the equation:

9(636 - 250) + 6(250) = 4974

5744 -2250 + 1500 = 4974

4974 = 4974

The equation balances, confirming that C. 250 is the correct answer.

To solve this problem, you need to use algebraic equations. Let's use the variable 'x' to represent the number of tickets sold to senior citizens. Here's the step-by-step process:

1. Calculate the number of tickets sold to non-senior citizens: 636 - x (since the total number of tickets sold is 636).

2. Calculate the revenue from non-senior citizen tickets: (636 - x) * $9.00.

3. Calculate the revenue from senior citizen tickets: x * ($9.00 - $3.00).

4. Set up an equation to represent the total revenue: (636 - x) * $9.00 + x * ($9.00 - $3.00) = $4974.

Let's solve this equation:

(636 - x) * $9.00 + x * ($6.00) = $4974
$5724 - 9x + 6x = $4974
-3x = $4974 - $5724
-3x = -$750
x = -$750 / -3
x = 250

So, the number of tickets sold to senior citizens is 250.

To find the correct answer from the given options, we subtract this value from the total number of tickets sold (636): 636 - 250 = 386 tickets sold to non-senior citizens.

Therefore, the correct answer is option A: 386.