The question, if I am right is in short, asking how many integers from 1 - 500 cannot be divided by both 5 and 3. That means, the least common multiple of 5 and 3 which is 15, and the rest of the multiples of 15 are out of the picture. So, what we do is, FIND THE NUMBER OF MULTIPLES OF 15 FROM 1- 500. In order to do that, we use this method:
{ [(number closest to 500 that is a multiple of 15) - (number closest to 1 that is a multiple of 15) ] divided by 15 } + 1 subtracted from 500 = ANSWER
Let us translate this to symbols:
[tex]500 - [ \frac{495 - 15}{15} + 1 ][/tex]
[tex]500 - [ \frac{480}{15} + 1 ][/tex]
[tex]500 - [ 32 + 1 ] [/tex]
[tex]500 - 33[/tex]
ANSWER:
467
