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.
b. Replace Stuttgart with Kiel.
c. Replace Berlin with Munich.
d. Replace Weisbaden with Hanover.
Answer (2)
Brendan should replace Stuttgart with Kiel to keep his costs under budget and closest to €860, resulting in a new cost of €858. This option is only €2 under the budget limit, making it the nearest possible adjustment. The original plan costed €946, so modifications need to reduce costs significantly.
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Calculate the original cost of the trip: 297 + 215 + 263 + 171 = 946 .
Evaluate each option to see which one is under €860.
Option b (€858) and option d (€852) are under €860.
Option b is closest to the budget of €860, so the answer is b .
Explanation
Analyzing the Problem Let's analyze Brendan's travel plans to minimize costs while staying close to his original budget.
Calculating Original Cost First, calculate the cost of Brendan's original plan, which includes visiting Stuttgart (€297), Dresden (€215), Wiesbaden (€263), and Berlin (€171). The total cost is: 297 + 215 + 263 + 171 = 946 So, the original plan costs €946.
Evaluating Options Now, let's evaluate each option to see which one keeps Brendan's costs under €860 and closest to his original budget.
Option A Option a: Replace Dresden (€215) with Potsdam (€179). The new cost is: 297 + 179 + 263 + 171 = 910 This option costs €910, which is over budget.
Option B Option b: Replace Stuttgart (€297) with Kiel (€209). The new cost is: 209 + 215 + 263 + 171 = 858 This option costs €858, which is under budget.
Option C Option c: Replace Berlin (€171) with Munich (€159). The new cost is: 297 + 215 + 263 + 159 = 934 This option costs €934, which is over budget.
Option D Option d: Replace Wiesbaden (€263) with Hanover (€169). The new cost is: 297 + 215 + 169 + 171 = 852 This option costs €852, which is under budget.
Finding the Closest Option Now, we need to determine which of the under-budget options (b and d) is closest to the original budget. The original budget was €946, but Brendan wants to keep costs under €860. Option b costs €858. The difference from the original cost is: 946 − 858 = 88 Option d costs €852. The difference from the original cost is: 946 − 852 = 94 However, we want to find the option closest to the original budget of €860. So, we calculate the difference from €860: For option b: 860 − 858 = 2 For option d: 860 − 852 = 8 Option b (€858) is closer to the budget of €860 than option d (€852).
Final Answer Therefore, the change that results in Brendan staying under budget and closest to his original budget is to replace Stuttgart with Kiel.
Examples
This problem demonstrates how to optimize travel plans based on a budget. In real life, you might use similar calculations to plan a road trip, considering factors like gas prices, accommodation costs, and activities. By comparing different routes and lodging options, you can create a cost-effective itinerary that maximizes your travel experience without exceeding your budget. This involves calculating the costs of different options and choosing the one that best fits your financial constraints, much like Brendan optimizing his city visits.
