Robyn and Shruti both run on the cross country team. Robyn runs 2 miles every day. Shruti starts her week with a 3-mile run and runs 1 mile every day, even on the day she runs the 3 miles. If M is the number of miles run during the week, and d id the number of days the girl has run this week, for which girl is the relationship between M and d multiplicative?
A. Shruti, because M = d +3
B. Shruti, because M = 3d
C. Robyn, because M = 2d
D. Robyn, because M = d + 2
Can someone show me how to solve?
Robyn: M = 2mi/day * d days = 2*d = 2d.
To solve this question, we need to understand the relationship between M (number of miles run during the week) and d (number of days the girl has run this week) for both Robyn and Shruti.
Let's start by analyzing Robyn's situation. We are given that Robyn runs 2 miles every day. So, the relationship between M and d for Robyn would be M = 2d.
Now let's analyze Shruti's situation. We know that Shruti starts her week with a 3-mile run and then runs 1 mile every day, even on the day she runs the 3 miles. So, the relationship between M and d for Shruti would be M = 3 + d.
To determine which girl has a multiplicative relationship between M and d, we can substitute possible values for d and calculate the corresponding values for M. If the relationship is multiplicative, then M should be a multiple of d.
Let's substitute d = 1. For Robyn, M = 2(1) = 2. For Shruti, M = 3 + 1 = 4. Here, M is not a multiple of d for either girl.
Now let's substitute d = 2. For Robyn, M = 2(2) = 4. For Shruti, M = 3 + 2 = 5. Again, M is not a multiple of d for either girl.
We can continue this process for larger values of d, but we can observe that for any given value of d, M will not be a multiple of d for either girl. Thus, neither Robyn nor Shruti has a multiplicative relationship between M and d.
Therefore, the correct answer is none of the provided options.