SOLUTION: The total cost of a taxi ride is the sum of a) A basic fixed cost for the first five miles b) An additional charge for every three miles after the first five. If the cost to t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: The total cost of a taxi ride is the sum of a) A basic fixed cost for the first five miles b) An additional charge for every three miles after the first five. If the cost to t      Log On


   

Question 550730: The total cost of a taxi ride is the sum of
a) A basic fixed cost for the first five miles
b) An additional charge for every three miles after the first five.
If the cost to travel 11 miles is $5, and the cost to travel 35 miles is $11, how many miles can you go with $7.25?
Please explain step by step, thanks.
Answer by TutorDelphia(193) About Me  (Show Source):
You can put this solution on YOUR website!
The total cost of a taxi ride is the sum of
a) A basic fixed cost for the first five miles which we will call b
b) An additional charge for every three miles after the first five which we will call a
Lets make mileage be m
In order to figure out the millage after the first 5 we can just do m-5.
But the charge is for every three miles so we have to do (m-5)/3
Our formula will be b+a*((m-5)/3)
If the cost to travel 11 miles is $5, and the cost to travel 35 miles is $11, how many miles can you go with $7.25?
For 11 miles (which cost 5 dollars)
5=b+a*((11-5)/3)
5=b+a*2
For 35 miles (which cost 11 dollars)
11=b+a*((35-5)/3)
11=b+a*10
Now we can use elimination method:
11=b+a*10
minus
5=b+a*2
6=a*8
a=6/8=3/4
now lets sub in for a
5=b+a*2
5=b+(3/4)*2
5=b+3/2
5=b+1.5
b=3.5
So our formula is now c=3.50+(3/4)*((m-5)/3)
So let's see how far we can go for 7.25
7.25=3.50+(3/4)*((m-5)/3)
3.75=(3/4)*((m-5)/3)=1/4*(m-5) (because the divided by 3 and the 3 in the numerator cancel out)
3.75=1/4*(m-5)
3.75*4=m-5
15=m-5
m=20