James and Kelvin started with the same amount of money. James spent $790 every month, while Kelvin spent $850. After a few months, James had $900 left, and Kelvin had 3/5 as much money left as James. We need to find out how much money Kelvin had at the beginning.

To solve this problem, we need to follow these steps:

1. First, we need to find out how much money Kelvin had left. Since Kelvin had 3/5 as much money left as James, we multiply $900 (the amount James had left) by 3/5. This gives us$540, which is the amount Kelvin had left.

2. Next, we need to find out how many months have passed. Since both James and Kelvin spent a fixed amount each month, and they started with the same amount of money, the number of months that have passed is the same for both of them. We can find this by subtracting the amount each person had left from the amount they spent each month. For James, this is $790 -$900 = -$110. For Kelvin, this is$850 - $540 =$310.

3. Since the number of months is the same for both James and Kelvin, we can set these two amounts equal to each other and solve for the number of months. This gives us -$110 =$310, or $420 =$420 when we add $110 to both sides. This means that 1 month has passed.

4. Finally, we can find out how much money Kelvin had at the beginning by adding the amount he spent in one month to the amount he had left. This is $850 +$540 = $1390.

So, Kelvin had $1390 at the beginning.