You are riding in a taxicab. At 1.5 miles, the fare on the meter is $4.55. At 3.2 miles, the fare is $7.78. How far can you travel if you have $35.00? Round your answer to the nearest tenth of a mile.
To solve this problem, we need to determine the fare per mile and then calculate how far you can travel with $35.00.
First, let's find the fare per mile. We can do this by finding the difference in fare between two distances divided by the difference in miles between them.
The fare at 3.2 miles is $7.78, and the fare at 1.5 miles is $4.55. So, the difference in fare is $7.78 - $4.55 = $3.23.
The difference in miles is 3.2 miles - 1.5 miles = 1.7 miles.
Now we can calculate the fare per mile: fare per mile = difference in fare / difference in miles = $3.23 / 1.7 miles ≈ $1.90 per mile.
Now, to find how far you can travel with $35.00, divide $35.00 by the fare per mile:
Distance = $35.00 / $1.90 per mile ≈ 18.42 miles.
Rounding to the nearest tenth of a mile, you can travel approximately 18.4 miles with $35.00.
an extra 1.7 miles cost an extra $3.23, so that's a rate of $1.90/mi
So, the cost for x miles is
c(x) = 1.90x + 1.70
so, set c=35.00 and solve for x