Question

an nyc taxi company charges a \\$2.50 flat rate in addition to a \\$0.50 per \\(\frac{1}{5}\\) of a mile. garrett has \\$15.00 to spend.

how far can garrett travel in the taxi?

a. less than or equal to 25 mi
b. more than or equal to 5 mi
c. more than or equal to 25 mi
d. less than or equal to 5 mi

Explanation:

🆕 New Concept Discovered: Solving Linear Inequalities in Word Problems
Translating real-world limits into inequality equations

Step 1: Find the cost per mile

The taxi charges \( \$0.50 \) per \( \frac{1}{5} \) of a mile. To find the cost for one full mile, we multiply the rate by \( 5 \):

$$ \text{Cost per mile} = \$0.50 \times 5 = \$2.50 \text{ per mile} $$

Step 2: Set up the inequality

Let \( x \) represent the number of miles Garrett can travel.

The total cost consists of a flat rate of \( \$2.50 \) plus \( \$2.50 \) per mile. Since Garrett has a maximum of \( \$15.00 \) to spend, the total cost must be less than or equal to \( \$15.00 \):

$$ 2.50 + 2.50x \le 15.00 $$

Step 3: Solve for \( x \)

Subtract the flat rate of \( 2.50 \) from both sides:

$$ 2.50x \le 12.50 $$

Divide both sides by \( 2.50 \):

$$ x \le \frac{12.50}{2.50} $$

$$ x \le 5 $$

This means Garrett can travel a distance less than or equal to \( 5 \text{ mi} \).

Answer:

D less than or equal to 5 mi