Final answer:
To find out how many applications Henry initially filled out, we set up an equation and solve for x. After simplifying the equation, we find that Henry initially filled out 14 applications.
Step-by-step explanation:
To find out how many applications Henry initially filled out, we can start by setting up equations based on the given information. Let's say the number of applications filled out by Henry initially is 'x'. Ben filled out 11 more applications, so Ben's initial number of applications would be 'x + 11'.
Both Henry and Ben filled out 5 additional applications each, which brings their total to 49. So, the equation becomes: x + (x + 11) + 5 + 5 = 49.
Simplifying the equation, we get: 2x + 21 = 49. Subtracting 21 from both sides, we have: 2x = 28. Dividing both sides by 2, we get: x = 14.
Therefore, Henry initially filled out 14 applications.