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Algebra / Linear equations in two variables Difficulty: Hard

A certain apprentice has enrolled in $85$ hours of training courses. The equation $10 x + 15 y = 85$ represents this situation, where $x$ is the number of on-site training courses and $y$ is the number of online training courses this apprentice has enrolled in. How many more hours does each online training course take than each on-site training course?

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Explanation

The correct answer is $5$ . It's given that the equation $10 x + 15 y = 85$ represents the situation, where $x$ is the number of on-site training courses, $y$ is the number of online training courses, and $85$ is the total number of hours of training courses the apprentice has enrolled in. Therefore, $10 x$ represents the number of hours the apprentice has enrolled in on-site training courses, and $15 y$ represents the number of hours the apprentice has enrolled in online training courses. Since $x$ is the number of on-site training courses and $y$ is the number of online training courses the apprentice has enrolled in, $10$ is the number of hours each on-site course takes and $15$ is the number of hours each online course takes. Subtracting these numbers gives $15 minus 10$ , or $5$ more hours each online training course takes than each on-site training course.