Final answer:
The smaller of two whole numbers with a quotient of 6 and a sum between 35 and 45 can only be 5, as it is the only number among the options given that satisfies the conditions when used to calculate the sum and the other number's size.
Step-by-step explanation:
The student has asked to find the smaller of two whole numbers given that their quotient is 6 and their sum is between 35 and 45. Using the given quotient, if the smaller number is x, the larger number must be 6x. Adding these together, we have x + 6x = 7x. The sum, 7x, must fall between 35 and 45.
Dividing 35 by 7, we get 5, and dividing 45 by 7 gives us a little over 6. So the smaller number x must be at least 5 but less than 6.5 to meet the conditions. Therefore, the only possible values from the options provided that fall in this range are 5 or 6. However, if x were 6, then 7x would be 42, which is within the required sum limit, but then the larger number would be 6x, which is 36, creating an impossible scenario where the smaller number is equal to the quotient. Thus, the only viable answer is 5.