At a state fair, attendees can win tokens that are worth a different number of points depending on the shape.

Question

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?

A.

$950$

B.

$90$

C.

$80$

D.

$10$

Accepted Answer

Choice D is correct. It&rsquo;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 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 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 - 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.

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