Question

the prices of tickets for the local rock concert were $16 for friday night and $28 for saturday night. the total attendance for the two nights was 1090. if the total receipts were $24,232, how many people attended saturday night?
a 251 people
b 524 people
c 566 people
d 1132 people

Explanation:

Step1: Define Variables

Let \( x \) be the number of people who attended Friday night, and \( y \) be the number of people who attended Saturday night. We know two equations:

1. \( x + y = 1090 \) (total attendance)
2. \( 16x + 28y = 24232 \) (total receipts)

Step2: Solve for \( x \) from the first equation

From \( x + y = 1090 \), we get \( x = 1090 - y \).

Step3: Substitute \( x \) into the second equation

Substitute \( x = 1090 - y \) into \( 16x + 28y = 24232 \):

$$ 16(1090 - y) + 28y = 24232 $$

Step4: Expand and simplify

$$ 17440 - 16y + 28y = 24232 \\ 17440 + 12y = 24232 $$

Step5: Solve for \( y \)

Subtract 17440 from both sides:

$$ 12y = 24232 - 17440 \\ 12y = 6792 $$

Divide both sides by 12:

$$ y = \frac{6792}{12} = 566 $$

Answer:

C. 566 people