ABC Taxi charges $1.75 plus 10¢ per mile while Friendly Taxi charges $2.25 plus 7¢ per mile. You want to know at what distance the two taxi companies would charge the same amount, and which company would be cheaper for shorter distances.
Looks like you need to setup an algebraic equation with one variable, d, for distance.
for example
1.75 + 0.10 d = 2.25 + 0.07 d
if you go zero miles, who is cheaper ?)
To find the distance at which the two taxi companies charge the same amount, we can set up an equation based on their pricing structures.
Let's represent the distance as "d" in miles.
For ABC Taxi, the total cost would be: $1.75 + ($0.10 * d) = $1.75 + $0.10d.
For Friendly Taxi, the total cost would be: $2.25 + ($0.07 * d) = $2.25 + $0.07d.
To determine when the two companies charge the same amount, we can set their total costs equal to each other:
$1.75 + $0.10d = $2.25 + $0.07d.
Next, we can solve this equation for "d" by isolating the variable:
$0.10d - $0.07d = $2.25 - $1.75.
$0.03d = $0.50.
Dividing both sides of the equation by $0.03, we find:
d = $0.50 / $0.03.
d ≈ 16.67 miles.
Therefore, at a distance of approximately 16.67 miles, both taxi companies would charge the same amount.
To determine which company would be cheaper for shorter distances, we can calculate the total cost for a specific distance, such as 5 miles, using the given pricing structures.
For ABC Taxi: $1.75 + ($0.10 * 5) = $1.75 + $0.50 = $2.25.
For Friendly Taxi: $2.25 + ($0.07 * 5) = $2.25 + $0.35 = $2.60.
For a 5-mile trip, ABC Taxi would be cheaper with a total cost of $2.25 compared to Friendly Taxi's total cost of $2.60.