Question

A taxi ride costs $5.50 plus $1.25 per mile driven. If Mr. Jones has $45 in cash, write an inequality to find the greatest whole number of miles he can ride in the taxi.

a) 5.50 + 1.25x ≥ 45
b) 5.50 + 1.25x ≤ 45
c) 5.50x + 1.25 ≥ 45
d) 5.50x + 1.25 ≤ 45

Answer 1

The correct inequality for determining how many miles Mr. Jones can ride in the taxi with $45 is 5.50 + 1.25x ≤ 45. The 'x' represents the number of miles, and the inequality signifies the maximum amount he can spend, accounting for the initial charge and per-mile rate. Additionally, the opportunity cost for bus tickets increases when the price doubles, affecting the budget constraint accordingly.

Step-by-step explanation:

To determine the greatest whole number of miles Mr. Jones can ride in the taxi with $45, we should use an inequality to represent the situation. The correct inequality to represent this scenario is 5.50 + 1.25x ≤ 45, where x is the number of miles he can ride. This inequality indicates that the initial charge of $5.50 plus the cost of $1.25 per mile should be less than or equal to the total amount of money Mr. Jones has, which is $45.

In this situation, to find the opportunity cost of bus tickets after the price increase from $0.50 per trip to $1 per trip, while the price of burgers remains at $2 and the budget is $10 per week, we note that the slope of the budget constraint represents the opportunity cost. Originally, the opportunity cost was calculated as $0.50/$2 = 0.25. After the price change, the new opportunity cost of bus tickets, when plotted on a graph, would be $1/$2 = 0.50.