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Test
Math
Domain
Algebra
Skill
Systems of two linear equations in two variables
Difficulty
Easy
ID: dba8d38a
Modded SAT Question Bank by Abdullah Mallik

A petting zoo sells two types of tickets. The standard ticket, for admission only, costs $5. The premium ticket, which includes admission and food to give to the animals, costs $12. One Saturday, the petting zoo sold a total of 250 tickets and collected a total of $2,300 from ticket sales. Which of the following systems of equations can be used to find the number of standard tickets, s, and premium tickets, p, sold on that Saturday?

  1. Equation 1: s plus p, equals 250. Equation 2: 5 s plus 12 p, equals 2,300.

  2. Equation 1: s plus p, equals 250. Equation 2: 12 s plus 5 p, equals 2,300.

  3. Equation 1: 5 s plus 12 p, equals 250. Equation 2: s plus p, equals 2,300.

  4. Equation 1: 12 s plus 5 p, equals 250. Equation 2: s plus p, equals 2,300.

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Correct Answer: A
Rationale

Choice A is correct. It’s given that the petting zoo sells two types of tickets, standard and premium, and that s represents the number of standard tickets sold and p represents the number of premium tickets sold. It’s also given that the petting zoo sold 250 tickets on one Saturday; thus, s plus p, equals 250. It’s also given that each standard ticket costs $5 and each premium ticket costs $12. Thus, the amount collected in ticket sales can be represented by 5 s for standard tickets and 12 p for premium tickets. On that Saturday the petting zoo collected a total of $2,300 from ticket sales; thus, 5 s plus 12 p, equals 2,300. These two equations are correctly represented in choice A.

Choice B is incorrect. The second equation in the system represents the cost per standard ticket as $12, not $5, and the cost per premium ticket as $5, not $12. Choices C and D are incorrect. The equations represent the total collected from standard and premium ticket sales as $250, not $2,300, and the total number of standard and premium tickets sold as $2,300, not $250. Additionally, the first equation in choice D represents the cost per standard ticket as $12, not $5, and the cost per premium ticket as $5, not $12.

Question Difficulty: Easy
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