Final answer:
The given scenario represents a linear relationship where the amount of money left decreases at a constant rate as the number of days increases. The equation that represents this relationship is L = I - (R * N), where L is the amount left, I is the initial amount, R is the rate of spending per day, and N is the number of days. Option A.
Step-by-step explanation:
The given scenario describes a situation in which a person is spending money at a constant rate and the amount of money left decreases linearly with the number of days that have passed. Therefore, this situation can be represented by a linear relationship.
To determine the equation that represents this relationship, we can use the given information. If Matthew is spending at the average of $5 per day, then the amount of money he has left after 10 days would be $15 less than what he initially had. So, we can set up the equation:
Initial amount - (Rate of spending per day * Number of days) = Amount left
Let's denote the initial amount as 'I', the rate of spending per day as 'R', the number of days as 'N', and the amount left as 'L'. Plugging in the given values, we can write the equation as:
I - (5 * 10) = 15
Simplifying the equation, we get:
I - 50 = 15
Adding 50 to both sides, we get:
I = 15 + 50
I = 65
Therefore, Matthew initially had $65. This linear relationship can be represented by the equation:
L = I - (R * N)
where L is the amount left, I is the initial amount, R is the rate of spending per day, and N is the number of days.
So Option A .