Final answer:
There are no three positive whole numbers with a mean of 4 and a range of 7.
Step-by-step explanation:
To find the three positive whole numbers with a mean of 4 and a range of 7, we can start by finding the middle number, or median. Since the mean is 4, we know that the sum of the three numbers is 12 (4 multiplied by 3). The middle number must be 4, so now we need to find the other two numbers that have a range of 7.
Let's assume the smallest number is x. Since x + 4 + the largest number = 12, we can conclude that the largest number is 8 - x. The range formula is the largest number minus the smallest number, so:
8 - x - x = 7
8 - 2x = 7
2x = 1
x = 0.5
Since we are looking for positive whole numbers, x cannot be 0.5. Therefore, there are no three positive whole numbers that satisfy the given conditions.