A taxi charges $.75 for the first quarter mile and $.35 for each additional mile. How far did Freddie ride if he paid no more than $7.40 for his taxi?
The bill for x + 1/4 miles is
.75 + .35x <= 7.40
To determine the distance Freddie rode, we can set up an equation based on the given information.
Let's denote the total distance Freddie rode as 'd' miles.
For the first quarter mile, Freddie was charged $0.75.
For the remaining distance (d - 0.25) miles, he was charged $0.35 per mile.
The total cost of the taxi ride can be expressed as:
Total Cost = Cost for first quarter mile + Cost for additional miles
Since the cost for additional miles is $0.35 per mile, we can calculate the total cost as follows:
Total Cost = $0.75 + ($0.35 × (d - 0.25))
According to the problem, Freddie paid no more than $7.40. Therefore, we can set up the following inequality:
Total Cost ≤ $7.40
Substituting the expression for the total cost into the inequality, we have:
$0.75 + ($0.35 × (d - 0.25)) ≤ $7.40
Now, let's solve the inequality to find the maximum distance Freddie can ride without exceeding $7.40.
$0.75 + ($0.35 × (d - 0.25)) ≤ $7.40
$0.75 + $0.35d - ($0.35 × 0.25) ≤ $7.40
$0.75 + $0.35d - $0.0875 ≤ $7.40
$0.35d + $0.6625 ≤ $7.40
$0.35d ≤ $7.40 - $0.6625
$0.35d ≤ $6.7375
d ≤ $6.7375 / $0.35
Now, let's divide $6.7375 by $0.35 to find the maximum distance Freddie can ride:
d ≤ $6.7375 / $0.35 ≈ 19.25
Therefore, Freddie can ride a maximum distance of approximately 19.25 miles without exceeding $7.40.