Paul has decided to take a trip to the United Kingdom. While he is there, he hopes to visit several different cities, which are shown in the table below. The table also includes how much money Paul expects to spend in each city, taking into consideration transportation, lodging, and so on. All costs listed are in pounds sterling ([tex]$£$[/tex]).
| City | Cost (£) |
| ----------- | ----------- |
| Bristol | 76 |
| Leicester | 66 |
| Glasgow | 91 |
| Leeds | 60 |
| Belfast | 72 |
Paul's sightseeing budget is [tex]$£ 300$[/tex]. What is the cheapest city that Paul can drop from his plans and still stay under budget?
a. Leicester
b. Leeds
c. Bristol
d. Belfast
Answer (2)
The cheapest city that Paul can drop from his travel plans while still staying under budget is Leicester, which costs £66. After calculating the total costs and the remaining amounts when excluding each city, all other options except Leeds keep him under budget, making Leicester the most affordable choice to drop.
;
Calculate the total cost of all cities: 76 + 66 + 91 + 60 + 72 = 365 .
Subtract each city's cost from the total to see which keeps Paul within his £300 budget.
Dropping Leeds results in a cost of £305, exceeding the budget.
Among the cities that keep him within budget, Leicester is the cheapest.
The cheapest city Paul can drop and stay within budget is Leicester .
Explanation
Calculate Total Cost First, let's determine the total cost of visiting all the cities on Paul's list. We add the costs for each city: Bristol (£76), Leicester (£66), Glasgow (£91), Leeds (£60), and Belfast (£72).
Total Cost Calculation The total cost is: 76 + 66 + 91 + 60 + 72 = 365 So, the total cost to visit all cities is £365.
Finding the Cheapest City to Drop Now, we need to find out which city Paul can drop to stay within his budget of £300. We will subtract the cost of each city individually from the total cost (£365) and see if the remaining cost is less than or equal to £300.
Calculating Remaining Costs
Dropping Bristol (£76): 365 − 76 = 289 The remaining cost is £289, which is within the budget.
Dropping Leicester (£66): 365 − 66 = 299 The remaining cost is £299, which is within the budget.
Dropping Glasgow (£91): 365 − 91 = 274 The remaining cost is £274, which is within the budget.
Dropping Leeds (£60): 365 − 60 = 305 The remaining cost is £305, which exceeds the budget.
Dropping Belfast (£72): 365 − 72 = 293 The remaining cost is £293, which is within the budget.
Identifying the Cheapest City From the calculations above, we see that if Paul drops Leeds, the remaining cost is £305, which is over his budget. However, if he drops any of the other cities, he will be within budget. We need to find the cheapest city among Bristol, Leicester, Glasgow, and Belfast that keeps him within budget. The costs of these cities are £76, £66, £91, and £72, respectively. The cheapest of these is Leeds at £60. However, dropping Leeds puts him over budget. The next cheapest is Leicester at £66.
Final Answer Since dropping Leeds puts Paul over budget, we need to consider the other options. Among the cities that keep him within budget (Bristol, Leicester, Glasgow, and Belfast), Leicester is the cheapest at £66.
Conclusion Therefore, the cheapest city that Paul can drop from his plans and still stay under budget is Leicester.
Examples
Budgeting is a common task in everyday life, from planning a vacation to managing household expenses. This problem demonstrates how to optimize a trip plan by removing the least expensive option to stay within a set budget. For example, if you have a grocery budget of $100 and a list of items costing $120, you would use a similar approach to determine which items to remove to meet your budget. This involves calculating the total cost, identifying items to cut, and ensuring the final cost is within the budget. This skill is valuable for making informed financial decisions and managing resources effectively.
