so the first plan charges 20 bucks a month plus $0.15 per minute, now the 20 bucks is a fixed value, usually just to keep the plan and other overhead charges, let's see how it goes it after a few minutes
1st minute.............20+0.15(1)
2nd minute.............20+0.15(2)
3rd minute.............20+0.15(3)
xth minute.............20+0.15x
second plan charges 35 bucks plus 10cents or $0.10 a minute, let's see how that goes
1st minute............35+0.10(1)
2nd minute............35+0.10(2)
3rd minute............35+0.10(3)
xth minute............35+0.10x
now, the the cost of the first one could be written as a cost function A(x) = 20+0.15x and the second one as a function B(x) = 35 + 0.10x.
for those two to be the same cost A(x) = B(x), so, what is x when that happens anyway?
[tex] \bf \begin{cases}
A(x)=20+0.15x\\
B(x)=35+0.10x
\end{cases}\implies \stackrel{\stackrel{\textit{costs are the same}}{A(x)=B(x)}}{20+0.15x=35+0.10x}
\\\\\\
0.15-0.10x=35-20\implies 0.05x=15\implies x=\cfrac{15}{0.05}\implies x=300 [/tex]
