Final answer:
To decide if a monthly subway pass is worthwhile, compare individual ride costs with the monthly pass cost using the inequality 1.25x > 35. If you take 45 rides a month, without the pass it costs $56.25, so purchasing the $35 pass saves money.
Step-by-step explanation:
Understanding Cost Analysis with Inequalities and Decision Making
To determine the number of times you must ride the subway for the monthly pass to be a better deal, you can set up an inequality. The cost per ride is $1.25, and the monthly pass is $35. We want to find the point at which the cost of individual rides exceeds the flat rate of the monthly pass. The inequality to represent this situation would be 1.25x > 35, where x is the number of rides. This inequality states that the cost of individual rides is greater than the cost of the monthly pass when you have taken more than the breakeven point of rides.
For question 2, if you ride the subway 45 times in a month without the monthly pass, your cost would be 1.25 * 45 = $56.25. Comparing this cost with the monthly pass, which is $35, you clearly see that buying the monthly pass saves you money. Therefore, for someone riding the subway 45 times a month, the decision is straightforward: You should buy the monthly pass.