ID: d7bf55e1
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)
Comment: The question seems designed to get students to create a system of equations. However, you can also use an average and basic arithmetic.
Method 1: If 30 tickets sold for a total of $300, then the average price per ticket was $10. Because the only two types of tickets cost $8 or $12, it must be true that an equal amount of each type of ticket was sold for the average price to be $10. Cut 30 in half, and we know that 15 adult tickets were sold. All we have to do is work out the details to answer the question about the amount spent on adult tickets.
15 * $12 = $180
The correct answer is 180.
Method 2: You can use Desmos to model and graph two lines. You can let x represent adult tickets and y represent children's tickets. Work out each equation bit by bit. One will track total cost, the other the total number of tickets sold.
The answer is 180.
Method 3: The textbook way of solving the question is to create the system of equations, as shown above in method 2, and deriving the solution with or without a calculator. You can be a little less rigid about using x and y, though.
$12 * number of adult tickets + $8 * number of children's tickets = $300
12a + 8c = 300
number of adult tickets + number of children's tickets = 30
a + c = 30
From here, you could either substitute or eliminate to isolate the number of adult tickets. I would probably eliminate if I were pursuing this route, since, as I have written in at least one other post, I have seen more students make mistakes using substitution.
8(a + c = 30)
8a + 8c = 240
12a + 8c = 300
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-4a = -60
a = 15
12 * 15 = 180
Regardless of how you arrive at the answer, it must be 180. This third method is okay to use, but once you have the fundamentals down, you have room to explore other options that might be more efficient.
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