Final answer:
The problem requires setting up an equation based on the given information and solving for x. There is no perfect match with the provided options, but choosing x = 2 yields a larger number 3x = 6. Option B (Smaller: 2, Larger: 6) is the closest approximation under the integer constraint.
Step-by-step explanation:
To solve the problem, we need to use the information given: One number is three times another. Let's denote the smaller number as x. Therefore, the larger number would be 3x. Then we are told that the larger number subtracted from 5 is less than the smaller number, which translates to the larger number subtracted from is 5 less than the smaller number. Therefore, we have the equation: 5 - 3x = x - 5.
Solving for x, we get:
- Add 3x to both sides of the equation to get 5 = 4x - 5.
- Next, add 5 to both sides of the equation to get 10 = 4x.
- Finally, divide both sides by 4 to find x = 2.5.
Since x is a whole number, none of the options presented exactly match our calculation, which means there might be an issue with the problem or the way it is interpreted. However, if we accept only integer values for x, the closest approximation from the options would be to choose 2 for the smaller number, which leads to 6 as the larger number. This satisfies the first part of the given information about one number being three times another, but it does not perfectly satisfy the second part of the statement. Therefore, the correct option, assuming integer values, would be B. Smaller: 2, Larger: 6.
However, it's essential to note that this solution slightly diverges from the strict interpretation of the presented problem, which did not yield an exact whole number result.