A math tutoring service opened for their first year open, it had 5 students. If 3 new students enroll each year, which of the following equations represents how many students will be enrolled in x years?
answer choices:
A: y = 5x - 3
B: y = 5x + 3
C: y = 3x + 5
D: y = 3x - 5
5 plus three times the number of years
5 + 3x
or
3x+5
To determine which equation represents the number of students enrolled in x years, we need to analyze the given information.
We know that the tutoring service had 5 students in its first year of operation. After that, 3 new students enroll each year. This implies that for each year, the number of students will increase by 3.
Let's consider the possible equations:
A: y = 5x - 3
B: y = 5x + 3
C: y = 3x + 5
D: y = 3x - 5
In equation A, the number of students (y) is represented as 5x minus 3. This equation suggests that the number of students decreases as time passes. Since the question states that 3 new students enroll each year, equation A does not align with the given information.
In equation B, the number of students (y) is represented as 5x plus 3. This equation implies that the number of students increases by 3 for each year. Since the question states that 3 new students enroll each year, equation B is a potential solution.
In equation C, the number of students (y) is represented as 3x plus 5. This equation indicates that the number of students increases by 5 for each year. However, the question states that 3 new students enroll each year, not 5. Therefore, equation C does not align with the given information.
In equation D, the number of students (y) is represented as 3x minus 5. This equation implies that the number of students decreases by 5 for each year. Since the question states that 3 new students enroll each year, equation D does not align with the given information.
Based on the analysis, the equation that aligns with the given information is B: y = 5x + 3. This equation represents that 5 students were enrolled in the first year, and 3 new students enroll each year thereafter.