Answer:
C. 335
Explanation:
We will need a system of equations to determine how many senior citizen tickets were sold, where
- A represents the quantity of adult tickets sold,
- and S represents the quantity of senior citizen tickets sold.
First equation:
The sum of the revenues earned from the adult and senior citizen tickets equals $8579.00:
(price of adult tickets * quantity) + (price of senior citizen tickets * quantity) = total revenue earned
Since adult tickets cost $22/adult, senior citizen tickets cost $13/senior citizen, and the total revenue earned is $8579.00, our first equation is given by:
22A + 13S = 8579
Second Equation:
The sum of the quantities of adult and senior citizen tickets equals the total number of ticket sold:
quantity of adult tickets + quantity of senior citizen tickets = total quantity of tickets sold
Since the theater sold 527 tickets in total, our second equation is given by:
A + S = 527
Method to Solve: Elimination:
We can solve for S by first eliminating. To eliminate A, we'll first need to multiply the second equation by -22:
Multiplying -22 by A + S = 527
-22(A + S = 527)
-22A - 22S = -11594
Now we can add this equation to the first equation to find S, the number of senior citizen tickets:
Adding 22A + 13S = 8579 to -22A - 22S = -11594:
22A + 13S = 8579
+
-22A - 22S = -11594
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(22A - 22A) + (13S - 22S) = (8579 - 11594)
(-9S = -3015) / -9
S = 335
Thus, 335 senior citizen tickets (answer C.)
Optional: Find A (the number of adult tickets sold) to check the validity of our answers:
We can find A by plugging 335 for S in any of the two equations in our system. Let's use the second one:
Plugging in 335 for S in A + S = 527:
(A + 335 = 527) - 335
A = 192
Thus, 192 adult tickets were sold.
Checking the validity of our answers:
Now we can check that our two answers for S and A are correct by plugging in 335 for S and 192 for A in both of the equations in our system and seeing if we get the same answer on both sides:
Plugging in 335 for S and 192 for A in 22A + 13S = 8579:
22(192) + 13(335) = 8579
4224 + 4355 = 8579
8579 = 8579
Plugging in 335 for S and 192 for A in A + S = 527:
192 + 335 = 527
527 = 527
Thus, our answers for S and A are correct.