Question 1050783: It takes Caroline 1 hr to ride the train to some place and 1.5 hr to ride the bus. Every week she must take at least 7 trips to the place, and she plans to spend no more than 9 hr in travel time. If a train trip costs $7 and a bus trip costs $2, how many times per week should she ride each in order to minimize cost?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! It takes Caroline 1 hr to ride the train to some place and 1.5 hr to ride the bus.
Every week she must take at least 7 trips to the place, and she plans to spend no more than 9 hr in travel time.
If a train trip costs $7 and a bus trip costs $2, how many times per week should she ride each in order to minimize cost?
:
let t = no. of train trips
let b = no. of bus trips
:
No. of trip equation
t + b = 7
t = -b + 7
:
The time equation
1t + 1.5b = 9
replace t with (-b+7)
(-b+7) + 1.5b = 9
1.5b - b = 9 - 7
.5b = 2
b = 2/.5
b = 4 bus rides
then
t = -4 + 7
t = 3 train rides
Find the cost
7(3) + 2(4) = $29
This would be the minimum cost, if she increase the bus to 5 times, her time would exceed 9 hrs: 5(1.5) = 7.5 hrs + train 2(2) = 9.5 hrs
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