Question

Alex is taking a taxi downtown. He only has $22.00 in his wallet. When the meter in the taxi is first turned on, it reads $3.00. As the taxi travels, $1.25 is added for each mile driven. Write an inequality to represent this situation, where m represents the miles driven. Which is the word problem used to find the maximum number of miles could Alex ride for $22.00?

A. 3 + 1.25m < 22
B. 3 + 1.25m > 22
C. 3 + 1.25m ≥ 22
D. 3 + 1.25m ≤ 22

Answer 1

Option A). The word problem used to find the maximum number of miles Alex could ride for $22.00 can be represented by the inequality 3 + 1.25m < 22. By solving this inequality, we can find the maximum number of miles Alex could ride for $22.00, which is 15 miles.

Step-by-step explanation:

The inequality 3 + 1.25m < 22 represents the word problem used to determine the maximum number of miles Alex may ride for $22.00. According to this disparity, the total fare ($3.00) plus the multiplier of $1.25 by the distance traveled (m) should not exceed $22.00. We can find the most miles Alex could ride for $22.00 by solving this inequality.

We can isolate 1.25m by subtracting 3 from both sides of the inequality. Using this, we get 1.25m < 19. To find m, we then divide both sides of the inequality by 1.25. The disparity decreases to m < 15.2. Thus, Alex's maximum riding distance for $22.00 would be 15 miles.