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24 votes
24 votes
If 2452 = 60q + 52r and q and r are possitive integers, give on possible value for q+r.

User Kfreezy
by
3.6k points

1 Answer

16 votes
16 votes

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

User Arminius
by
3.0k points
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