Final answer:
There are 133 positive integers between 100 and 499 that are divisible by 3.
This is found by determining the smallest and largest multiples of 3 in this range and using a formula to count the number of terms.
Step-by-step explanation:
The question asks to find how many positive integers between 100 and 499 inclusive are divisible by 3.
To solve this, we need to find the smallest and largest multiple of 3 within this range.
The smallest multiple of 3 greater than or equal to 100 is 102 (since 100 divided by 3 leaves a remainder of 1, and 101 leaves a remainder of 2, but 102 is exactly divisible by 3).
The largest multiple of 3 less than or equal to 499 is 498 (since 499 divided by 3 leaves a remainder).
To find the number of multiples of 3 in this range, we use the formula (largest multiple - smallest multiple) / 3 + 1.
Therefore, the calculation will be (498 - 102) / 3 + 1, which equals (396 / 3) + 1, giving us 132 + 1, which equals 133.
There are 133 positive integers between 100 and 499 that are divisible by 3.