A limousine service charges
$20
plus
$0.50
per mile and a taxicab company charges
$1.50
per mile. Write and graph a system of equations for the cost of each ride, find the number of miles for each ride to cost the same, and determine which would be cheaper if a rider has to go
30
miles.
Let x = miles.
$20 +$.50x = $1.50x
Solve for x, then substitute 30 for x.
To find the cost of each ride, we can write a system of equations. Let's denote the cost of a limousine ride as L and the cost of a taxicab ride as T.
The limousine service charges a flat fee of $20 and an additional $0.50 per mile. So, the cost of a limousine ride can be calculated using the formula:
L = $20 + ($0.50 * miles)
On the other hand, the taxicab company charges $1.50 per mile. So, the cost of a taxicab ride can be calculated using the formula:
T = $1.50 * miles
To find the number of miles for each ride to cost the same, we need to set the cost equations equal to each other and solve for "miles":
L = T
$20 + ($0.50 * miles) = $1.50 * miles
Now, let's solve this equation for "miles":
$20 = $1.50 * miles - $0.50 * miles
$20 = $1 * miles
miles = $20
Therefore, the number of miles for each ride to cost the same is 20 miles.
Now, let's determine which would be cheaper if a rider has to go 30 miles. We can substitute this value into the cost equations and compare the results:
For the limousine ride:
L = $20 + ($0.50 * 30) = $20 + $15 = $35
For the taxicab ride:
T = $1.50 * 30 = $45
Comparing the costs, we can see that the limousine ride would be cheaper for a 30-mile trip, costing $35 compared to the taxicab ride costing $45.