SOLUTION: MUSClebound Movers charges $85 plus $40 an hour to move households across town. Champion Moving charges $60 an hour for cross-town moves. For what lengths of time is Champion more

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Question 298799: MUSClebound Movers charges $85 plus $40 an hour to move households across town. Champion Moving charges $60 an hour for cross-town moves. For what lengths of time is Champion more expensive? Show your work and explain your answer
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
MUSClebound Movers charges $85 plus $40 an hour to move households across town.
Champion Moving charges $60 an hour for cross-town moves.
For what lengths of time is Champion more expensive?
:
Let t = no. of hrs
:
MB Movers Cost = 40t + 85
and
Champ Mover Cost = 60t
:
60t > 40t + 85
:
60t - 40t > 85
:
20t > 85
t >
t > 4.25
:
We can say when t = 5 hrs, Champ is more expensive
:
:
:
A $3.00 toll is charged to cross the bridge from Sanibel Island to mainland Florida.
A six-month pass, costing $15.00, reduces the toll to $0.50.
A one-year pass, costing $150, allows for free crossings.
How many crossings per year does it take, on average, for the two six-month
passes to be the most economical choice?
Assume a constant number of trips per month.
:
let n = number of crossings per year
:
Cost with no pass = 3n
:
The 2 ea 6 months passes cost equation
c = .50n + 2(15)
c = .50n + 30
:
Cost when using the 1 yr pass = $150, unlimited no. of passes
:
no pass > 2 ea 6 mon passes
3n > .50n + 30
3n - .5n > 30
2.5n > 30
n >
n > 12 trips and then the 6 month pass is a better deal
and
6 mon passes cost > unlimited pass cost
.50n + 30 > 150
.5n > 150 - 30
.5n > 120
Multiply both sides by 2
n > 240 trips (6 mon pass is a better deal up to 240 trips a year)
:
Summarize: Greater than 12 and less than 240 trips the 2 ea 6 mon passes is best