5
algebra

A theater sold 300 tickets for a play. Adult tickets cost $12 and student tickets cost $8. Total revenue was $2,800. How many adult tickets were sold?

A

100 adult tickets

B

150 adult tickets

C

125 adult tickets

D

175 adult tickets

Correct Answer: A

Choice A is the correct answer. Let aa = adult tickets and ss = student tickets.

Step 1: Set up the system: {a+s=30012a+8s=2800\begin{cases} a + s = 300 \\ 12a + 8s = 2800 \end{cases}

Step 2: From first equation: s=300as = 300 - a

Step 3: Substitute: 12a+8(300a)=280012a + 8(300 - a) = 280012a+24008a=280012a + 2400 - 8a = 28004a=4004a = 400a=100a = 100

Solution: 100 adult tickets (and 200 student tickets)

Verification: 100+200=300100 + 200 = 300 ✓ and 12(100)+8(200)=1200+1600=280012(100) + 8(200) = 1200 + 1600 = 2800

💡 Strategic Tip: Revenue problems: tickets × price = total revenue.

Choice B is incorrect because 12(150)+8(150)=1800+1200=3000 eq280012(150) + 8(150) = 1800 + 1200 = 3000 \ eq 2800.

Choice C is incorrect because 12(125)+8(175)=1500+1400=2900 eq280012(125) + 8(175) = 1500 + 1400 = 2900 \ eq 2800.

Choice D is incorrect because 12(175)+8(125)=2100+1000=3100 eq280012(175) + 8(125) = 2100 + 1000 = 3100 \ eq 2800.