Final Answer:
There are 40 whole numbers between 100 and 300, inclusive, that are divisible by both 2 and 5.
Step-by-step explanation:
Firstly, identify the multiples of 10 within the given range of 100 to 300. The first multiple of 10 within this range is 100, and the last multiple is 300. To find the count, use the formula:
\(\text{Count of multiples} = \frac{\text{Last multiple} - \text{First multiple}}{\text{Common difference}} + 1\).
For this range, it becomes \(\frac{300 - 100}{10} + 1 = \frac{200}{10} + 1 = 20 + 1 = 21\).
However, these multiples of 10 include every number divisible by 2 and 5, but there's a need to exclude numbers divisible by their least common multiple, 10, more than once (i.e., numbers divisible by 10 * 2 = 20 and 10 * 3 = 30).
To do that, identify how many numbers are divisible by 20 and 30 within this range. Counting the multiples of 20: \(300 / 20 = 15\). Counting the multiples of 30: \(300 / 30 = 10\).
Subtract these extra counts from the initial count of multiples of 10: \(21 - (15 + 10) = 21 - 25 = -4\). However, it can't be a negative count, so it's corrected to \(0\).
Therefore, the total count of numbers divisible by both 2 and 5, between 100 and 300, inclusive, is \(21 - 0 = 21\). However, be cautious in other scenarios as the exclusion might result in a non-zero value.