Let x be the number of miles the family travel.
We know that company A charges a fee of $70.50 plus $0.15 per mile, then the total cost in company A is:
[tex]0.15x+70.50[/tex]Now, company B charges a fee of $45.50 plus $0.10 per mile, then the total cost in company B is:
[tex]0.10x+45.50[/tex]To find how much more does A charges, we substract the expression B to the expression A, then:
[tex]\begin{gathered} (0.15x+70.50)-(\text{0}.10x+45.50)=0.15x+70.50-0.10x-45.50 \\ =0.05x+25 \end{gathered}[/tex]Therefore company A charges
[tex]0.05x+25.00[/tex]more for x miles.