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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?

Verified Answer :

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 220 is the charge
if your mileage is 50miles, when 250 is the charge
if your mileage is 1000miles, when 21000 is the charge
if your mileage is "m" miles, when 2m 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 320 is the charge
if your mileage is 50miles, when 350 is the charge
if your mileage is 1000miles, when 31000 is the charge
if your mileage is "m" miles, when 3m 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

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