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Algebra / Linear equations in two variables Difficulty: Medium

At a state fair, attendees can win tokens that are worth a different number of points depending on the shape. One attendee won $S$ square tokens and $C$ circle tokens worth a total of $1,120$ points. The equation $80 S + 90 C = 1,120$ represents this situation. How many more points is a circle token worth than a square token?

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Explanation

Choice D is correct. It’s given that the equation $80 S + 90 C = 1,120$ represents this situation, where $S$ is the number of square tokens won, $C$ is the number of circle tokens won, and $1,120$ is the total number of points the tokens are worth. It follows that $80 upper S$ represents the total number of points the square tokens are worth. Therefore, each square token is worth $80$ points. It also follows that $90 upper C$ represents the total number of points the circle tokens are worth. Therefore, each circle token is worth $90$ points. Since a circle token is worth $90$ points and a square token is worth $80$ points, then a circle token is worth $90 minus 80$ , or $10$ , more points than a square token.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect. This is the number of points a circle token is worth.

Choice C is incorrect. This is the number of points a square token is worth.