Question

1. you are selling tickets for a high school play. student tickets cost $4.00 and general admission tickets cost $6.00. you sell 525 tickets and collect $2,876.00. how many of each type of tickets did you sell?

137 student tickets and 388 adult tickets
137 adult tickets and 388 student tickets
212 student tickets and 313 adult tickets
100 student tickets and 425 adult tickets

Explanation:

Step1: Check total tickets for each option

For an option with \( s \) student tickets and \( a \) adult tickets, total tickets should be \( s + a = 525 \).

• Option 1: \( 137 + 388 = 525 \) (good)
• Option 2: \( 137 + 388 = 525 \) (good, but labels reversed)
• Option 3: \( 212 + 313 = 525 \) (good)
• Option 4: \( 100 + 425 = 525 \) (good)

Step2: Check total revenue (\( 4s + 6a = 2876 \))

• Option 1: \( 4(137) + 6(388) = 548 + 2328 = 2876 \) (matches)
• Option 2: \( 4(388) + 6(137) = 1552 + 822 = 2374 \) (no)
• Option 3: \( 4(212) + 6(313) = 848 + 1878 = 2726 \) (no)
• Option 4: \( 4(100) + 6(425) = 400 + 2550 = 2950 \) (no)

Answer:

137 student tickets and 388 adult tickets