Final answer:
The two numbers in question are 11 and 44, where 11 is the smaller number and 44 is the larger number that is 4 times as large as the smaller one.
Step-by-step explanation:
The question asks for us to find two numbers whose sum is 55, with one number being 4 times larger than the other. Let's start by defining the smaller number as x and the larger number as 4x, since it is four times as large. The sum of these two numbers, as given by the problem, is 55.
Therefore, the equation to solve is x + 4x = 55. Combining like terms gives us 5x = 55. Dividing both sides by 5 to isolate x gives us x = 11. This is the smaller number. To find the larger number, we multiply 11 by 4, which gives us 44 as the larger number.
The two numbers are 11 and 44.