Answered

Jake is planning a trip to China. He has made a list of cities he would like to visit, as well as the approximate amount of money he plans to spend in each as a result of travel, lodging, shopping, and so on. All costs are listed in renminbi (¥).




City		Cost (¥)

Tianjin		557

Nanjing		681

Zhengzhou		595

Beijing		728

Wuhan		449

Chengdu		534






Unfortunately, Jake only has ¥2,920 available. What is the cheapest city that Jake can remove from his travel plans and still stay under budget?


ATianjin
BWuhan
CNanjing

Verified Answer :

  • Calculate the current total cost of the trip: \(557 + 681 + 595 + 728 + 449 + 534 = 3544\) ¥.
  • Evaluate the impact of removing the suggested cities: Tianjin, Wuhan, and Nanjing.
  • Find the remaining costs: Removing Tianjin leaves \(2987\) ¥, Wuhan leaves \(3095\) ¥, and Nanjing leaves \(2863\) ¥.
  • Identify the only option that brings the total under the budget of \(2920\) ¥: removing Nanjing.
  • Final answer: \(\boxed{\text{c}}\)

Explanation

  1. Analyzing Current Total Cost

To determine which city Jake should remove to stay within his budget of \(2920\) ¥, we first calculate the total cost of his current travel plan. The costs for the cities are: Tianjin (557 ¥), Nanjing (681 ¥), Zhengzhou (595 ¥), Beijing (728 ¥), Wuhan (449 ¥), and Chengdu (534 ¥). The total cost is:
\[557 + 681 + 595 + 728 + 449 + 534 = 3544 \text{ ¥.}\]
Since \(3544 > 2920\), Jake must remove at least one city from his list to meet his budget constraint.

  1. Calculating Remaining Costs After Potential Removals

Jake is considering three options for removal: Tianjin (557 ¥), Wuhan (449 ¥), and Nanjing (681 ¥). We calculate the remaining total cost for each option by subtracting the city's cost from the original total of \(3544\) ¥:

  • If removing Tianjin: \(3544 - 557 = 2987\) ¥.
  • If removing Wuhan: \(3544 - 449 = 3095\) ¥.
  • If removing Nanjing: \(3544 - 681 = 2863\) ¥.
  1. Conclusion and Selection

We now compare the remaining costs to the budget of \(2920\) ¥:

  • Removing Tianjin: \(2987 > 2920\) (Still over budget).
  • Removing Wuhan: \(3095 > 2920\) (Still over budget).
  • Removing Nanjing: \(2863 \leq 2920\) (Within budget).

The only option that results in a total cost under the budget is removing Nanjing. Therefore, since Nanjing is the only one among the provided choices that brings the trip within the budget, it is the correct city to remove.

Examples

This problem illustrates how to perform budget management using basic arithmetic and logical selection. In real-life scenarios, such as planning vacations, monthly household expenses, or allocating funds for a business project, identifying which costs to reduce or eliminate is crucial for staying within a defined financial limit. By calculating the total impact of each possible reduction, one can make an informed decision that satisfies both financial constraints and personal preferences.