Acar rental company's standard charge includes an initial fee plus an additional fee for each mile driven. the standard charge s (in dollars) is given by the function =s+0.60m18.95, where m is the number of miles driven. the company also offers an option to insure the car against damage. the insurance charge i (in dollars) is given by the function =i+0.15m3.70 . let c be the total charge (in dollars) for a rental that includes insurance. write an equation relating c to m. simplify your answer as much as possible.

Lets see... we have two companies charging two different prices.  So, the first thing we need to do if find the equation of both companies. Company A: c= 0.25m+30       m is the number of miles, which costs .25 cents.  Hence, .25mCompany B: c= 0.10m+40      it charges 10 cents per mile, which is 0.10 m Now, make the two equations equal to each other.  The answer that we get will be the exact number when you pay the same cost for either company A or B.  In other words, at that number of miles you don't care which company you choose.  However, if you go beyond that number of miles or below that number of miles, it will make a difference. 0.25m+30=0.10m+40     Subtract 30 from both sides          -30              -300.25m=     0.10m+10      Subtract 0.10m from both sides  -0.10m    -0.10m0.15m= 10                      Divide both sides by 0.15     m= 66 2/3   Up to that point, company A will be the best choice.  After that particular number of miles, company B will be the better choice. Hope this helps you.

~ Natalia