SOLUTION: Method of Substitution 11. Pietro needs to rent a truck for 1 day. He calls two rental companies to compare costs. Joe's Garage charges $80 for the day plus $0.22/km. Ace Trucks c

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Method of Substitution 11. Pietro needs to rent a truck for 1 day. He calls two rental companies to compare costs. Joe's Garage charges $80 for the day plus $0.22/km. Ace Trucks c      Log On


   

Question 181743: Method of Substitution
11. Pietro needs to rent a truck for 1 day. He calls two rental companies to compare costs. Joe's Garage charges $80 for the day plus $0.22/km. Ace Trucks charges $100/day and $0.12/km. Under what circcumstances do the two companies charge the same amount? When would it be better for Pietro to rent from Joe's Garage.
Thank you very much and i need it today please.
Answer by Mathtut(3670) About Me  (Show Source):
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Method of Substitution
11. Pietro needs to rent a truck for 1 day. He calls two rental companies to compare costs. Joe's Garage charges $80 for the day plus $0.22/km. Ace Trucks charges $100/day and $0.12/km. Under what circcumstances do the two companies charge the same amount? When would it be better for Pietro to rent from Joe's Garage.
Thank you very much and i need it today please.
:
1)Joes: C=.22(k)+80.......where C is the cost and k is the km driven
:
Ace: C=.12(k)+100.........where C is the cost and k is the km driven
:
2)for joe to be equal to Ace we just set the equations equal and solve for k
:
.12(k)+100=.22(k)+80
:
.1k=20
:
highlight%28k=200%29km.......this is the amount of kilometers that makes the costs equal
:
3) now we are looking for Joe < Ace
:
which we write as .22k+80<.12k+100
:
.1k<20
:
highlight%28k%3C200%29km.....so as long as kilometers stay under 200 Joe will be the cheaper cost. they are equal at 200 and over 200km Ace will be the lower cost