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university theater sold 527 tickets for a play. Tickets cost $22 per adult and $13 per senior citizen if total receipts were 8579 how many senior citizens tickets were shown?? A.282 B.192 C.335 D. 245

1 Answer

3 votes

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

----------------------------------------------------------------------------------------------------------

(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.

User Bazza
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