Question: You are purchasing a new cell phone plan, and know you want the unlimited texting option. Plan A costs $0.20 per minute and $10 a month for the texting. Plan B costs $0.15 per minute and $25 a month for the texting.

a) Let \(A\left( m \right)\) and \(B(m)\) be the total cost (in dollars) of using your phone for m minutes under plan A and plan B respectively. Find equations for \(A(m)\,and\,B(m)\).

b) Use algebra (working by hand) to determine when the conditions under which each plan would be the better choice. Explain your reasoning.