Question

Pablo only has $39.47 (at max) for a trip downtown. The cab ride has an initial fee of $4.00 with a $0.32 charge for every half mile.Which inequality could determine the distance can Pablo travel? (use m for every half mile)

Answer 1

To determine the distance Pablo can travel, let's first break down the cost structure of the cab ride:

1. The initial fee for the cab ride is $4.00.
2. There is an additional charge of $0.32 for every half mile traveled. If we let \( m \) represent the number of half miles traveled, the cost for this distance is \( 0.32m \).

The total cost \( C \) of the cab ride can be expressed as:
\[
C = 4.00 + 0.32m
\]

Pablo's budget for the trip is a maximum of $39.47. To find out how far he can travel, we can set up the inequality to ensure that the total cost does not exceed his budget:
\[
4.00 + 0.32m \leq 39.47
\]

Now, let's isolate \( m \) in the inequality:

1. Subtract \( 4.00 \) from both sides:
\[
0.32m \leq 39.47 - 4.00
\]
\[
0.32m \leq 35.47
\]

2. Divide both sides by \( 0.32 \):
\[
m \leq \frac{35.47}{0.32}
\]

This gives us the inequality:
\[
m \leq 110.84
\]

Since \( m \) represents the number of half miles Pablo can travel, it must be a non-negative integer. Therefore, the complete inequality that represents the maximum distance in half miles that Pablo can afford is:
\[
m \leq 110
\]

In conclusion, the final inequality that determines the distance can Pablo travel is:
\[
4.00 + 0.32m \leq 39.47
\]