Final answer:
The correct division problem that meets the criteria is 450 ÷ 20 with a remainder of 10. This number was chosen by strategically adding the remainder to a multiple of the divisor which is a 3-digit number.
Step-by-step explanation:
The question you've asked involves creating a division problem that has a 3-digit dividend, a divisor of 20, and a remainder of 10. To construct such a problem, we must find a 3-digit number that, when divided by 20, leaves a remainder of 10.
The key to solving this is to realize that the remainder is always less than the divisor. Since our divisor is 20 and the remainder must be 10, we can start with a number that is divisible by 20 and then add the remainder to it. Let's take a multiple of 20, like 420, which is a divisible 3-digit number, and add the remainder of 10 to get 430. Now our division problem looks like this: 430 ÷ 20 which gives us a quotient and a remainder of 10.
However, none of the options you've given follow this path. Option A: 310 is not a multiple of 20 plus 10. Option B: 530 also is not a multiple of 20 plus 10. Option C: 420 does not need an additional 10 to be divisible by 20. Option D is correct, as 450 ÷ 20 will give us a quotient and a remainder of 10 when the 10 is strategically added to the divisible number 440.