Posted by lil on Wednesday, April 10, 2013 at 7:24pm.
how many integers, x, for which x/2, x/3 and x/5 is also an integer can be found between 1 and 500? help me!!

algebra  Reiny, Wednesday, April 10, 2013 at 8:28pm
the number must be divisible by 2, by 3, and by 5
that is it must be divisible by 30
So the sequence is
30 60 90 ... < 500
this is an arithmetic sequence, where
a = 30 and d = 30
what term is around 500
a+ (n1)d = 500
30 + (n1)(30) = 500
30 + 30n  30 = 500
30n = 500
n = 16.66
so n = 16 , because 17 would be more than 500
check:
term(16) = 30 + 15(30) = 480
there are 16 such numbers