Brendan is planning a trip to Germany. He is trying to decide which cities to visit during his stay. The following table shows potential cities he could visit, as well as what he expects to pay for lodging, transportation, and similar expenses in each one. All costs are given in euros (€).
| City | Cost (€) |
|---|---|
| Berlin | 171 |
| Wiesbaden | 263 |
| Hanover | 169 |
| Dresden | 215 |
| Kiel | 209 |
| Stuttgart | 297 |
| Potsdam | 179 |
| Munich | 159 |
Brendan's original plan was to visit Stuttgart, Dresden, Weisbaden, and Berlin. However, he would like to keep his costs under €860. Which change to Brendan's travel plans would result in his staying under, but closest, to his original budget?
A. Replace Dresden with Potsdam.
Answer (2)
Brendan's original trip costs €946, which exceeds his budget of €860. By replacing Dresden with Potsdam, the new trip cost is €910, reducing the budget overage to €50. Thus, the best option to stay closest to his budget is to choose the revised plan with Potsdam.
;
Calculate the original cost of the trip: 297 + 215 + 263 + 171 = 946 .
Calculate the cost of the trip with the change (replacing Dresden with Potsdam): 297 + 179 + 263 + 171 = 910 .
Determine how much the original plan exceeds the budget: 946 − 860 = 86 .
Determine how much the new plan exceeds the budget: 910 − 860 = 50 . Since €50 is less than €86, replacing Dresden with Potsdam brings the cost closer to the budget, but still exceeds it. However, among the given options, it's the closest to the budget.
The change that results in his staying under, but closest, to his original budget is replacing Dresden with Potsdam.
Explanation
Calculate Original Cost First, we need to calculate the original cost of Brendan's trip, which includes Stuttgart, Dresden, Wiesbaden, and Berlin. The costs for each city are: Stuttgart (€297), Dresden (€215), Wiesbaden (€263), and Berlin (€171). So, the original total cost is:
Sum the Costs 297 + 215 + 263 + 171 = 946
Consider the Change The original cost of the trip is €946, which is over Brendan's budget of €860. Now, let's consider the proposed change: replacing Dresden with Potsdam. The cost of Potsdam is €179. So, the new itinerary includes Stuttgart (€297), Potsdam (€179), Wiesbaden (€263), and Berlin (€171). The new total cost is:
Calculate New Cost 297 + 179 + 263 + 171 = 910
Calculate Difference from Budget - Original Plan The new cost of the trip is €910, which is still over Brendan's budget of €860. To determine which plan is closest to the budget, we need to calculate how much each plan exceeds the budget. For the original plan, the amount over budget is:
Original Plan Exceeds Budget 946 − 860 = 86
Calculate Difference from Budget - New Plan For the new plan (replacing Dresden with Potsdam), the amount over budget is:
New Plan Exceeds Budget 910 − 860 = 50
Conclusion Replacing Dresden with Potsdam results in a cost that is €50 over budget, while the original plan is €86 over budget. Therefore, replacing Dresden with Potsdam brings the cost closer to the budget.
Examples
Understanding how to manage a budget and make informed decisions based on cost is crucial in everyday life. For example, when planning a home renovation, you might have an initial plan that exceeds your budget. By comparing costs of different materials or contractors, you can adjust your plan to stay within your financial limits, similar to how Brendan adjusted his travel plans. This involves calculating the original cost, considering alternatives, and comparing the differences to find the option that best fits your budget.
