Problema Solution
1. In Raleigh the price of a ride share for a 5.2 mile ride is $12.60 and the price for a 2.8 mile ride is $8.40.
a. Identify the independent and dependent variables.
b. Determine the slope and interpret its meaning in the context of the problem.
c. Determine the linear function.
d. Predict your distance traveled with the ride share if you bill is $21.96. Round to 0.01 miles.
e. If you travel 3.75 miles what is the cost of your trip? Round to $0.01.
Answer provided by our tutors
Let
y = the cost of the trip (dependent variable)
x = the number of miles crossed (independent variable)
We will assume that the equation for the cost is linear, that is:
y = mx + b, where m is the slope and the charge of the ride per mile, and b is the fixed start fee charged.
Using the info from the text we have 2 points from the line given (12.60, 5.2) and (8.40, 2.8):
12.60 = 5.2m + b
8.40 = 2.8m + b
........
click here to see the system of equations solved for m and b
........
m = 7/4
b = 7/2
The linear equation is:
y = (7/4)x + 7/2
d. If the bill is $21.96 then this means that y = 21.96 and we need to find x:
21.96 = (7/4)x + 7/2
(7/4)x + 7/2 = 21.96
........
click here to see the equation solved for x
........
x = 10.55 mi
The distance traveled was 10.55 miles.
e. If you travel 3.75 miles what is the cost of your trip? Round to $0.01.
We need to find y when x = 3.75:
y = (7/4)*3.75 + 7/2
y = $10.06
The cost for 3.75 miles trip is around $10.06.