You can use variables to represent how many applications Henry filled which will then help to find how many applications did Ben filled initially.
Ben originally filled 11 forms.
Henry originally filled 5 forms
When the amount is to be known which is not given, then in most cases, you can use variables. These are placeholder symbols who can be used to work further on those values.
Lets assume that Henry filled originally [tex]x[/tex] forms.
Then. as Ben originally filled 6 more forms than Henry, thus we can represent the number of forms filled by Ben as [tex]x + 6[/tex] (the +6 shows 6 more forms along with [tex]x[/tex] number of forms)
It is given that when each of them filled 4 additional forms, then total filled forms were 24
Thus, Count of total forms filled by Henry = [tex]x[/tex] + 4 additional forms = [tex]x + 4[/tex]
Count of total forms filled by Ben = [tex]x+6[/tex] + 4 additional forms =[tex]x + 6 + 4 = x + 10[/tex]
Total forms filled by both = Forms by Henry + Forms by Ben
[tex]24 = (x+4) + (x +10)\\24 = (x+x) + 4+10\\24 = 2x + 14\\\\\text{Subtracting 14 from both the sides}\\\\24 - 14 = 2x + 14-14\\10 = 2x\\\\\text{Dividing by 2 on both the sides so that x is left alone}\\\\\dfrac{10}{2} = \dfrac{2x}{2}\\\\5 = x\\x=5[/tex]
Thus,
Henry filled out initially [tex]x = 5[/tex]forms
And Ben filled out 6 more forms than Henry = [tex]x + 6 = 5 + 6 = 11[/tex]
Learn more about variables here:
https://brainly.com/question/967776
