Final answer:
To find the value of variable M when variable p is 16, we first determine the constant of variation when M is 75 and p is 10. After finding the constant as 7.5, we multiply this by the new value of p to get M, resulting in 120.
Step-by-step explanation:
The student's question is about discovering the value of the variable M when the variable p changes value while maintaining a direct variation relationship. From the provided information, M = 75 when p = 10, and we need to find the value of M when p = 16.
First, we need to find the constant of variation. Since M varies directly with p, we have M = kp, where k is the constant of proportionality. With M = 75 when p = 10, we can determine k by dividing M by p:
k = M/p
k = 75/10
k = 7.5
Then, we use this constant to find M when p = 16:
M = 7.5 × p
M = 7.5 × 16
M = 120
So, when p equals 16, the value of the variable M is 120.