Answer:
q+r may be any of 41, 43, 45, 47
Explanation:
You want possible positive values of q and r such that 2452=60q+52r.
Trial and Error
We observe that subtracting 52 from 2452 gives a result (2400) that is divisible by 60. Hence one possible solution is ...
q = 40, r = 1 . . . . . q+r = 41
Other values
We know that this equation can be reduced by dividing it by 4 to get ...
613 = 15q +13r
This means that increasing the value of r by 15 and decreasing the value of q by 13 will give another solution. We can continue to do that while we have positive values for both variables. That means there are 4 possible solutions:
{q, r} = {40, 1}, {27, 16}, {14, 31}, {1, 46}
Then possible sums are ...
q+r = 41, 43, 45, 47