I have between 30 and 50 pennies. when I put them in piles of 5 there is still one left over. when put them in piles of 4s, I have one penny left over. how many pennies do I have?

If you put them in piles of 5, then it could be:

30

35

40

45

50

but you have one left, so it could be then

31

36

41

46

51

if you put them in piles of 4 then it would be:

32

36

40

44

48

and if one is left then

33

37

41

45

49

and the only number both of those with one left in the ppile is 41!