Let's turn that into a linear system:
Set the equations equal to each other and solve:
We then plug in to get
:
The solution to the system is
.
Now, let's turn our attention to the statements.
The first one is
false: Emilia's rate is higher, and the two plans cost the same at 50 texts, after which point Hiroto's plan becomes
cheaper!
The second one is also
false: we already figured out that the lines intersect at
.
The third statement is also
false: as above, the lines intersect at
.
The fourth statement is
true: the lines intersect at
.
In conclusion, the fourth statement - "Both plans cost the same when 50 texts are sent" - is true.