The science club needs to rent a bus for a field trip. main street buses charges a $40 rental fee, plus $2 per mile. county bus line charges a $20 rental fee, plus $3 per mile. for what number of miles will the total charges be the same? what will that charge be?

M = Main Buses
C = County Buses

so the charges from Main are $40 fee, then additional $2 for every mile you drive it for, so   M = 40 + 2m
if your mileage is 20miles, when 2*20 is the charge
if your mileage is 50miles, when 2*50 is the charge
if your mileage is 1000miles, when 2*1000 is the charge
if your mileage is "m" miles, when 2*m is the charge

and County charges are $20 fee, then additional $3 for every mile... .so then C = 20 + 3m
if your mileage is 20miles, when 3*20 is the charge
if your mileage is 50miles, when 3*50 is the charge
if your mileage is 1000miles, when 3*1000 is the charge
if your mileage is "m" miles, when 3*m is the charge

so, their total charge is M and C respectively
when are the charges equal?  well, when M = C
or 
40 + 2m = 20 + 3m

solve for "m", to see at how many miles that happens

what will the charge be?  plug that value for "m" on either, to get the charge