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Algebra / Linear equations in two variables Difficulty: Hard

$5 G + 45 R = 380$

At a school fair, students can win colored tokens that are worth a different number of points depending on the color. One student won $G$ green tokens and $R$ red tokens worth a total of $380$ points. The given equation represents this situation. How many more points is a red token worth than a green token?

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Explanation

The correct answer is $40$ . It's given that $5 G + 45 R = 380$ , where $G$ is the number of green tokens and $R$ is the number of red tokens won by one student and these tokens are worth a total of $380$ points. Since the equation represents the situation where the student won points with green tokens and red tokens for a total of $380$ points, each term on the left-hand side of the equation represents the number of points won for one of the colors. Since the coefficient of $G$ in the given equation is $5$ , a green token must be worth $5$ points. Similarly, since the coefficient of $R$ in the given equation is $45$ , a red token must be worth $45$ points. Therefore, a red token is worth $45 minus 5$ points, or $40$ points, more than a green token.